Combo bursts celebrate achieving a combo milestone by flashing a combo burst image. Said images are different for each game mode.
For osu!, osu!taiko, and osu!catch, stars will shoot out from either the left or right side of the playfield for combos less than 100x, then both sides simultaneously for combos 100x or higher. For osu!mania, the stars will shoot out from the left and right sides of the stage.
Note: Combo bursts can be disabled in the options.