Frame Walking is a glitch that allows Mario to walk up steep slopes that would normally cause him to slip and slide.
It is done by alternating between no input on the joystick and using the joystick to walk up the slope. The optimal method is 1 frame no input, and 1 frame walking up the slope. However it is not frame perfect, and multiple frames can be taken with each of them although this is slower.
Frame walking works by taking advantage of the fact that Mario will not start sliding on a steep slope until his speed reaches 0. However, when Mario decelerates and then begins walking again, if his speed is less than 8 it is set to 8. Because of this, Mario never begins sliding and can walk up the slope.
Frame walking does not work on slippery slopes, which cause Mario to slide down even if frame walking is attempted.
Frame walking is primarily used in challenges such the A Button Challenge. The glitch allows Mario to reach areas otherwise inaccessible without jumping.