From the Super Mario Wiki
The Target is an object in the Super Smash Bros. series. It is featured in the bonus stage Break the Targets! in 1-player mode in Super Smash Bros. and Classic Mode in Super Smash Bros. Melee. The target also has a trophy in Melee, which can be obtained by beating the Target test with all characters. The target's single purpose is being hit by the player. Targets can be broken with even the weakest of attacks, but are not affected by grabs of grabbing moves. Sometimes a target moves around or warps to another location, making them more difficult to hit and break. Targets are always present as a group of ten in each Break the Targets! stage.
In Super Smash Bros. Brawl, they will be colored differently depending on the difficulty level. Level 1 - Blue, Level 2 - Green, Level 3 - Yellow, Level 4 - Orange, and Level 5 - Red.
In Super Smash Bros. for Nintendo 3DS / Wii U, there is a mode called Target Blast. Here players earn points by breaking targets and objects.