Anti-Air refers to hitting the opponent out of the air, when you are in a grounded position and they are jumping at you. It can also refer to moves that are good at this purpose.
Anti-Air is important in fighting games, because the majority of attacks will not beat a jump-in attack. This means that jumping will beat 90% of grounded attacks. The tradeoff for this power is, jumping is slow. If you are not doing something when they jump, you can see the jump coming and shut it down. So technically, jumping is beaten by waiting and having good reaction times.
So which moves are actually good Anti-Air? These tend to be moves with hitboxes that are up higher than the hurtboxes of the character, such as Crouching Hard Punch on Ryu. These can also be invincible moves that come out quickly and have an upwards trajectory, such as Shoryuken on Ryu. Not all invincible moves are necessarily good anti-airs, because if they come out too slowly, or hit too low to the ground, they may allow the opponent to land and block before it becomes active.
Be careful with timing normal anti-airs as they tend not to be as active as invincible uppercut moves. Normal anti-airs tend to be the more important option to learn, as you can press one button really quickly and easily when you see an anti-air. Special anti-airs tend to be based more on prediction, and are riskier if you throw them out and the opponent doesn't jump. A good trick for anti-airing consistently is if you don't know when they'll jump, just wait and do a normal anti-air when they do, and if you do know when they'll jump, do the motion for the special anti-air, but also check the air simultaneously for whether they're jumping or not. When you're done inputting the motion, only press the button to activate the special if they actually jumped while you were inputting, this way if they didn't jump, you can just not press the button and avoid risking anything. Good players can do the whole motion on reaction to a jump without needing to use this trick, though it's still helpful to have. Even for good players, it's important to have consistency at both normal and special anti-airs.
Another way you can anti-air opponents is by taking advantage of Trip Guard. Trip Guard protects you by allowing you to block during landing animations, but if they attack in the air, they're not allowed to block during their landing. So using an appropriately spaced low move, such as a sweep, can low profile the jump-in attack and catch them without Trip Guard. This is referred to by most as a Trip Guard Anti-Air.
Another technique is jumping at opponents just before they attack, and air-throwing them. Air Throws come out instantly and have big hitboxes, meaning they tend to beat other air attacks in most games.
Some games have moves that are invincible to air attacks, like all medium uppercut specials in Street Fighter V, crouching H in Dragon Ball FighterZ, and a lot of forward As in Blazblue. Forward Punch in Guilty Gear grants upper body invincibility, which can be used for anti-air or a lot of other purposes.
Getting consistent at anti-airing is one of the first steps towards consistently defending yourself, so it's something important to practice whenever you start a new fighting game. Try recording a dummy to jump at you. If the game has multiple recording slots, make the dummy wait longer or shorter during different recordings, so you can't tell when it will jump, and you need to anti-air on reaction.