Perhaps you are curious how people find new combos, what a combo is, or how to determine which moves combo, or what separates a good combo from a bad combo. From the outside looking in, it can appear like fighting games are just about memorizing these random combos the developers came up with to deal a lot of damage whenever you land a hit, but in reality, there is actually a reasonably simple system that governs how moves can combo, which allows people to research and develop new combos with different advantages, such as damage, corner carry, reset potential, meter gain, ending in knockdown, or other purposes. Also the combo used will change based on the starting move, the position on-screen, and how much meter you currently have. Viewed from overhead, combos are less like pre-determined sequences, and more like a tree of possible moves that can connect differently based on circumstance.
How do Moves Combo?
Put most simply, a combo is when you hit your opponent before they recover from the hitstun of a previous move. Every time you hit your opponent it will interrupt whatever state they're currently in, starting up an animation called hitstun. During hitstun, they have no ability to perform any actions. If you hit an opponent before their hitstun ends, there is nothing they can do to stop you, thus this is a combo. Incidentally, hitting them while they are in hitstun causes another hitstun animation to play as a result of the move you just hit them with, so it is possible to choose a sequence of moves that each deal enough hitstun to allow another followup.
Link Combos
The most simple type of combo is a Link (though it's generally the hardest to perform). A Link is simply a move that has frame advantage followed by a move that has a short startup. As long as the frame advantage of the first move is more than the startup of the second move, these two moves will combo as a link. You can cross-reference this easily and quickly on a frame data table by simply looking for any move with a high frame advantage on hit, and all the moves with a lower startup time than that.
To perform a link, you simply hit them with one move, then perform the next move as soon as the first move recovers. The tricky part is that the timing window on this may be extremely tight, even as tight as 1 frame. More modern games, such as Street Fighter V usually have buffers in place to make link combos easier. A good tip for practicing link combos is, if the second move comes out but does not combo, then you are pressing the button too late. If the second move does not come out at all, you are pressing the button too early. You must press exactly when the first move has fully recovered.
Cancel Combos
The simplest to perform type of combo is a Cancel, especially a Chain Cancel. In a cancel, the window to successfully combo is the entire duration of hit freeze when a move connects, which is typically around 10 frames. If you input the next move during this time, it will be held onto and performed immediately when Hit Freeze ends. This means with most characters in most games, you can do basic combos easily by simply looking up which moves cancel and which ones don't.