Button-mashing (occasionally “spamming”) is the act of hitting buttons (or any inputs) rapid-fire.
There are two useful kinds of button-mashing: you can be pressing the same button or type of button over and over again in order to activate a special move, or in order to increase the power of certain special moves, or perhaps to make a difficult input easier; or, you may be literally mashing your hand over all the buttons (and perhaps moving the stick as well) in order to flood the buffer (which is usually only useful in a handful of situations dictated by the game system).
The term “button-mashing” is often used disparagingly, but this is only true of someone who really doesn’t know what they are doing when they press so many buttons at once.
Pressing the same button repeatedly activates some special moves in some games: E. Honda’s Hyakuretsu Harite, Chun-Li’s Hyakuretsu Kick, Blanka’s Electric Thunder, Joe Higashi’s Bakuretsuken, Billy’s Senpūkon, Ralf and Clark’s Vulcan Punch, and Jang’s Tekkyū Daikaiten are all the prime examples.
In other cases, mashing the same class of button adds a certain number of hits to some moves; Ibuki’s Kasumi Suzaku and Ken’s Shinryūken both do this.
Mashing all the inputs as fast as you can comes into play for certain moves and situations. In the Samurai Shodown series, there will come certain times when the weapons clash, and both duelists will be engaged in a battle of strength; whoever hits the most buttons total wins, so it is important to press as much as you can at those points. Likewise, most games (starting with SFII) will let you recover from a dizzy state faster the more you mash the buttons. Certain kinds of throws that amount to strangling (found in many games, also starting with SFII) will attack faster and be escaped later if the aggressor mashes the buttons better, and will attack slower and be escaped sooner if the defender mashes the buttons better.