A combo is a series of successive hits which are usually hard to break out of. Combos first appeared in Street Fighter II, where they were discovered as an accidentally overlooked exploit: specifically, the game's method of 'reading' the player input to make special moves easier to perform had the side effect of allowing special attacks to be performed in the midst of a normal attack(s). This allowed the player to perform said special attacks so quickly that an opponent would not be able to recover before another move struck them. This would later be known as cancelling.
Since the advent of Street Fighter II, almost every fighting game in the genre has used a similar formula as a deliberate gameplay formula. From Super Street Fighter II onwards, the game will keep track of combos and show rewards onscreen, awarding points for the amount of hits in the combo and type of attacks used.
Depending on the character used, combos can be crucial to learn. Combo videos are common throughout the web, particularly YouTube; they showcase powerful combos used in Street Fighter and other fighting games.
In the Street Fighter games, the most basic method of initiating a combo is to jump at an opponent and land a heavy air attack. This can then be followed up with another hit on the ground, before the opponent can recover.
Usually, the next step is to perform a cancel: for example, Ryu can perform a standing or crouching uppercut and then cancel into either a Hadoken or a Shoryuken, creating a basic but powerful 3-hit combo, which the opponent will be unable to block or escape if the first hit connects cleanly.
Various games in the franchise expand upon this by introducing Chain Combos, which are a specific series of regular attacks that can be canceled into each other, juggles, and allowing the canceling of special attacks into Super Combos or Ultra Combos. There are other methods that players use to string together successful combos, including hit confirming.
However, the basic principle always remains the same: using a series of attacks that cannot be defended against once the first attack connects.