Yo-hand notation is used in trick descriptions so that both left-handers and right-handers can follow them. For the right-handed yo-yoer their right hand is their yo-hand and for a left-handed yo-yoer their left hand is their yo-hand. The other hand is referred to as the non-yo-hand or the free-hand (not to be confused with the Duncan Freehand yo-yo or the freehand style).
Weaknesses of yo-hand notation
Yo-hand notation tends not to be used in 2A or 3A due to the fact both hands hold a yo-yo and often do the same thing. It is also awkward in some freehand tricks due to the counterweight changing hands so the yo-hand becomes the non-yo-hand and things become complicated.
The other difficulty with yo-hand notation is when certain directions are needed that are different for left-handers to right-handers. For example, many (but not all) tricks that involve a clockwise movement for a left-hander will require an anti-clockwise movement for a right hander. When directions like these are necessary it is usually best to say what left-handers and right-handers do separately to make things clear before continuing with yo-hand notation.
On account of the fact that "Yo-hand" is a terrible pun, one popular alternative is to use the terms "throwhand" and "non-throwhand," respectively. In fact, many might argue that these terms are more commonly used than "Yo-hand."