In pixel based video games, sub-pixel refers to a sprite having an x or y coordinate that is not reflected on the video display. For example, if the sprite is located at screen position x=128, 129 or 130, it will display in all cases as being at screen position x=128.
In a platform game like Super Mario Bros., sub-pixel can be very important, although they are unseen by the player. A jump might be possible to land if Mario jumps from x position 129, but not from x position 128. In these cases, whether a player can make the jump involves on intuition or more likely, luck. This is especially the case for executing glitches like wall jumping or clipping. In Tool Assisted Speedruns, where the sub-pixel value can be ascertained with a high level of certainty, jumps and glitches become easy to perform.