Next pieces are pieces that will occur after current piece. Some older games gave a bonus if you had the next piece turned off.

S is next

Most games show 3 or 6 next pieces, although the Tetris Guideline states that there can be any number from 1 to 6 next pieces. All "dollar-store type" Tetris games found everywhere on Internet show 1 next piece. This was also common in older games, like Tetris (Game Boy).