Chain Kombos
Kombo Attacks are a sequence of Normal Moves that can be strung together with the proper button sequence. Every character has several Kombo Attacks, and each character's Kombo Attacks are unique. Knowing your Kombo Attacks just requires memorization.
Kombo Attacks will get you more damage than Normal Moves alone. They are also very useful in Juggle Combos, as many Kombo Attacks are designed so that all hits juggle against airborne opponents very conveniently. They are also excellent for pressure, as quite a few Kombo Attack strings, when purposefully not completed, will give you pressure opportunity if the opponent blocks your attacks.
Kombo Attack Leniency
The window for performing Kombo Attacks is pretty lenient when it comes to timing. In fact, there is almost no pernalty for doing Kombo Attacks too quickly. For example, Scorpion has a Kombo Attack of Forward + Back Punch into Front Punch into Back Kick. You can literally hold Forward on the controller and press all three buttons in the sequence before the first attack even connects, and the entire chain combo will execute.
It's more likely that you'll perform the Kombo Attack too slowly. Generally speaking, if the attack has connected and you hit the button a little after that, the next move in the sequence won't come out. So if you are going to perform the Kombo Attack, you're better off inputting the commands quickly. However, this does make for difficulties when it comes to hit confirmation as you do not want to commit to a Kombo Attack that leaves you vulnerable if the opponent blocks it, so you may have to perform it a little slowly so you can stop before the last hit if the opponent is blocking, but generally you commit to the entire string ahead of time.
Kombo Attack Komboability
Generally speaking, if you ever try to combo a Special Attack off of a Normal Move, the Special Attack will not connect. However, this is not the case when it comes to Kombo Attacks. As long as the move is any hit in the series of buttons that isn't the last hit, canceling into a Special Attack will combo (unless the Special Attack is particularly slow). For example, Scorpion has a Kombo Attack sequence of Front Punch into Front Punch into Front Punch. All three hits are bufferable, but if you perform all three attacks against a grounded opponent and buffer into the Spear, the Spear will be blockable by the opponent even though it connects during hit Stun. However, if you cancel the first Front Punch OR the second Front Punch, because they are part of a Kombo Attack chain and not the last move, buffering them into a Spear will indeed connect.
In general, the rule is: if the opponent is grounded, always cancel before the last hit of the chain in order for your Special Attack to connect as a combo. When Juggling, however, it doesn't matter and as long as the moves reach, they will combo against an airborne opponent.