There are multiple forms of advantage, each of which should not be disregarded in a match (as long as you have the time to consider it - see the section on mental advantage for some reasons you might struggle to do so!), and each of which is a group of several similar mechanics that interrelate strongly - different forms of advantage will still affect each other, but not quite so strongly.
There are reasons to give up advantage, many of your options throughout a match will be trading advantage for dealing damage. Consider the common mixup between throwing and comboing! Throwing maintains initiative, comboing loses that initiative but deals more damage, and both are needed as components of the mixup for either to be usable.
When you look back on your decisions you should consider the advantage gain or cost, and whether it was worthwhile. Did you need to press that button there? Could you have just waited for a moment, let them choose between multiple bad options, and punished accordingly? This is often a strong option as your opponent will rarely respond with the correct counterplay of great patience.
Note that this is not the same thing as pressure - applying pressure can be thought of as a way of spending advantage to deal damage.
If you've experienced being trapped in the corner by Degrey while he repeatedly punches you, you likely have some idea about this one. It governs how close you are to the corner, which of your opponent's attacks they can get you with, how much you're backing off (are you blocking too early and losing ground? are you backing off from round start while they just walk up to you?). This is why just walking forward can be the most powerful move, or the greatest mistake.
It is heavily impacted by how much "pushback" each character has in a matchup - for example, Valerie has a huge amount of pushback versus Lum, because he has to spend so long blocking while she gets to attack him and push him into the corner. The character with more pushback can be expected to gain positional advantage over time, forcing their opponent to manage their position very carefully and take advantage of other things.
This is especially critical versus Argagarg and Degrey, as both are very good at pushing you into the corner. Lose this by being knocked back by a move, or backing off (eg, to defend), or crossing up into disadvantage (eg, to mixup). Regain this by pushing forward or crossing up into advantage.
Surprisingly, this is not just about the round timer - this is about how much you're taking advantage of every second you get that your opponent isn't attacking you. Are you missing opportunities to toss items as Lum? Are you failing to cancel into your specials as Argagarg? Then you're giving up time advantage. Have you just knocked down your opponent? Then you're taking it back, keep doing that!
This is important for every character, but some care more than others - Valerie spends most of her time moving and attacking, so if she's positioned correctly and the opponent's knocked down there's not much more she can do to take advantage of it. If you're fighting Midori then this becomes significantly more important.
This is especially critical versus Midori, as he will inevitably reach dragon form. Lose this by spending time doing nothing (eg, to leave yourself open to react), doing useless moves (eg, to cover an opponent's option), and being knocked down. Regain this by hitting or knocking down your opponent.
Initiative is a more general one, based on the current state of the game. If you're trading projectiles and they're clashing closer to you than your opponent, that's disadvantaged initiative, if you're knocked down, that's disadvantaged initiative, if you're performing a mixup with positive EV, that's advantaged initiative.
Consider your initiative with every decision you make - advantaged initiative is very powerful and allows you to pressure your opponent very safely, whereas disadvantaged initiative leaves you vulnerable and stuck on the defensive. Common forms of initiative include Grave repeating his jA/jB mixup, Rook repeating his throw mixup, and dragon Midori existing.
Lose this by your opponent hitting you with a move with frame advantage, getting into their character's main attack patterns, or knocking you down. Gain this by doing these things to your opponent.
State is the general state of the game. Consider whether you have your super available, how much health you have, the state of any meters your character might have. If you're, say, ahead on super meter, that's advantaged state. If you're Grave and have no wind meter, that's less advantaged state.
This is relevant to the outcomes of any given situation - if you're fighting Lum and they use jackpot and get four minilums, and you have wind available, that situation is far more in your favour than if you didn't. If you're Rook, how much health you have dictates your ability to rely on armour.
A major aspect of state is resource management - if you choose to desperately use super at the end of one round and lose, the state will favour you less at the start of the next when you lack super.
A notable example of state where your opponent has an amount of health equal to the damage dealt by one of your tools, giving you huge advantage in any situation where that tool is available. This is especially significant with trades, which will now instead win the round.
In particular, it's possible now for a checkmate tool to exist, where no option they might use will win the round. If only one unsafe option might win the round, that might also be referred to as a checkmate, though victory is less assured - usually these are chip setups.
If you are in a checkmate or near-checkmate situation, you may be forced to "play to your outs", defined as follows: If you only have one way to even possibly win, do it! If something has to go right for you to have any hope of victory, assume it will!
Mental advantage isn't a facet of the game, but rather the player. If you're overwhelmed, desperate, or have decision fatigue, you have mental disadvantage. If your opponent does, you have mental advantage.
This can be manipulated by certain patterns - for example, Lum's items overwhelm the opponent more effectively than most moves, so tossing out an item first makes your opponent more likely to let you throw them on their wakeup. Similarly, jumping over someone might cause them to instinctively throw you, in which case you have a way to get a safe yomi counter if you use it sparingly enough that they don't adapt.
Gain this by confusing the opponent or exhausting them. Lose this by making complicated decisions or going into unfamiliar situations.
There are multiple situations that perfectly encapsulate specific forms of advantage, and considering these dynamics will hugely aid your understanding of advantage. Here are a few: