From the Super Mario Wiki
Smash Coins are special types of coins found in Super Smash Bros. Melee and Super Smash Bros. Brawl. In these games, there is a special kind of match called Coin Battle. Whenever a player takes damage, these Smash Coins fly out, to be collected by the players.
In Super Smash Bros. Melee, gold Smash Coins are worth ten, silver are worth five, and bronze are worth one. Whenever a player gets KO'ed, he or she loses half of their coins (rounded down). The player with the most Smash Coins when time runs out wins.
Smash Coins reappear in Super Smash Bros. Brawl in the Coin Battle. However, there are also Smash Bills appearing. The values of the Smash Coins are different in this game. Gold coins are worth six Smash Coins, silver coins are worth three, and bronze coins are worth one. The Smash Bills are worth ten Smash Coins each.
Coin Battle returns in Super Smash Bros. for Wii U, with the coins and bills the same purpose as it did in previous games.
Super Smash Bros. Melee
Super Smash Bros. Brawl