When I see new players try a 3D fighting game such as Soul Calibur or Virtua Fighter, they often have trouble understanding advantage time. The concept matters in 2d fighting games like Street Fighter and Guilty Gear as well, but because 2d games tend to have so much emphasis on zoning and controlling space, advantage time is more of a concept for intermediates or experts, rather than a thing beginners get crushed by. (They are too busy getting crushed by fireball traps or rushdown!)
What is Advantage Time?
In a fighting game, advantage time is the length of time (usually measured in 1/60ths of a second, called frames) that you recover from your attack *before* the opponent recovers from blocking (or getting hit by) your attack. If you do a kick, then the opponent blocks it, you have to recover from your kick (that takes some time) and your opponent gets briefly locked into "blockstun" (a state where they are stuck blocking) and that takes time for them to recover from, too. If you recover 3 frames sooner than the opponent in this situation, we say that you have 3 frames of advantage time. If instead the opponent recovers 3 frames first, most charts of frame data will call that "-3 advantage time" though in spoken English you could just say the opponent has 3 frames of advantage time.
Why does this matter so much?
If after a blocked attack, you recover a few frames before the opponent, that means if you both immediately do a move, yours will probably win. Your move will come out sooner and get to the active/hitting part before his, if the moves were the same speed.
In 3D fighting games, beginners can get totally destroyed by advantage time tricks without even knowing what's going on. The opponent does some moves, then it seems like it's the beginner's "turn" to do something, but whatever he does gets beat out. He's probably attacking in a situation where he has frame disadvantage, but he doesn't even know it.
Nitaku / Forced Choice / 2-Choice Situations
In 3D fighting games, there's a term called 2-choice (or "nitaku") situation which means you put the opponent in a bad situation where he must choose between 2 things, and the deck is stacked against him, so to speak. If he's attacking from big frame disadvantage (your last attack recovered way sooner than his blockstun or hitstun recovered) then he has to worry about you possibly thowing him if he just stands there, or getting hit by a mid attack if he crouches to avoid the throw. If he guesses wrong, he's going to take damage.
What if he guesses right though? If he guesses right by blocking high or low correctly, notice that he did no actual damage to you. Here, his correct guesses dealt no damage while your correct guesses do deal damage. He could also guess correctly by attacking and hitting your throw attempt. That's great and all, but attacking from frame disadvantage is a dangerous choice on his part. It will come out ok for him if you happen to try to throw (his attack will win), but if you attack also, it's going to be pretty bad for him. First, your attack will almost certainly win because yours will start sooner (that's what frame advantage means). Second, you will interrupt his attack--not just hit him while he's standing there. When you interrupt an opponent's attack in a 3D fighting game (or some 2d fighting games), that's called a Major Counter and depending on the game, comes with juicy bonuses against the victim. It means a bigger combo or more damaging hit. So attacking from frame disadvantage can end up being more painful than just standing there and getting hit.
Frame Advantage in 2D Games
As I said before, frame advantage in 2D games is less important than in 3D because 2D games often have ranged battles where one character is struggling to get close in the first place. Advantage time doesn't matter much in those situations, it's more about zoning / spacing. Even though it matters less than in 3D figthing games, it still matters though. There are still plenty of tricks and uses of advantage time and it's still very important to know at the intermediate level and above.
Regarding advantage time, one big difference between 2D and 3D fighting games is the existence of nearly instant attacks like dragon pucnhes. My discussion of 2-choice situations above (in 3D fighting games) assumed that neither player has access to a dragon punch attack--they are uncommon in 3D fighting games. By "dragon punch attack," I mean an attack that is invulnerable at the start and hits almost right away. If you had such a move, you could use it even if you are attacking from frame disadvantage and you'd still hit the opponent's move.
This leads to a common trick among expert 2D fighting game players: giving up advantage time ON PURPOSE. By doing a move that (on block) leaves you at frame disadvantage, it baits the opponent to attack you. Players who are at least at the intermediate skill level will probably not be able to stop themselves from attacking, because it feels like a natural time. That's when you can do your dragon punch or super move as a surprise. One way to use this trick is to get right up next to the opponent, do a normal move (often a stand fierce or strong or something in Street Fighter), let it recover, then dragon punch or super. Notice that if you did a move that left you with advantage time, then you immediately dragon punched, your move might come out before the opponent even had a chance to do anything. So the trick here is to give up advantage time to trick the opponent into committing, then doing a dragon punch or super.
That's a nice trick, but what you really want is a more stable strategy, rather than a gimmick. The more stable strategy is to get frame advantage as often as you can (which means knowing which moves give it) and to attack in that situation often. Not attack EVERY time, because you'd be opening yourself up to dragon punches, but still to attack often.
In Guilty Gear, one example is Chipp's close standing slash. It gives Chipp 2 frames of advantage time on block, so he can do it once, wait for it to recover (don't chain into the automatic second hit), then do the close standing slash again. Opponents are often afraid and try to do something after the first blocked hit because instinctively they are used to getting advantage time in such situations, but not on this particular move. If they try to do their own normal attack, they will get hit (Major Countered, even) and then get combo'd.
Another way to get advantage time that comes up all the time is to do a "meaty attack." That means to stick out an attack early against an opponent who is getting up from a knockdown (or other unhittable state) such that end your attack hits, rather than the beginning. This is good because if the end of your attack hits, that means you're almost recovered already. You'll almost certainly recover from your move before the opponent exits blockstun.
If you actually hit with a meaty attack, you get so much advantage time that you can usually combo into another hit, guaranteed. At the very least, you can use almost any meaty attack (remember: hitting with the tail-end of an attack as an opponent gets up) to ensure you recover before they opponent's blockstun ends. This means the opponent is more likely to continue blocking, which means you can then sometimes attempt to throw. This is a weaker (but still good) version of the nitaku situation I discussed earlier from 3D fighting games. The opponent at frame disadvantage has a worse set of options, so he's often forced to just block while you keep up your offense.
Meaty Attacks + Dragon Punches
Ken (from ST and HD Remix) is an interesting exmaple because of his knee bash throw. After this throw (a "hold" actually) the opponent ends up standing, not knocked down. Ken can do a variety of tricks here, including a meaty attack. Ken actually doesn't even care that much if the attack he does after the knee bash leaves him at frame advantage or disadvantage. Either way, if you attack he can dragon punch (he might wait a few frames as a bait if he left himself at frame disadvantage). Just about anything you do will get beat by his dragon punch, effectively resetting the situation so that Ken can try it again. If you don't attack, Ken can knee bash you again for good damage, and threaten to repeat the situation.
This is another example of a 2-choice situation where the outcomes are overall really good for the attacker. Notice how having a dragon punch move means that attacker has more margin of error when it comes to advantage time. If he has it, great. If he doesn't he can still dragon punch, and in this case, that results in not just damage, but also in setting up another 2-choice situation in your favor.
Hopefully this gives you some sense of what advantage time is, and why many players comb the frame data charts looking for ways to exploit it.