Foremost, “hold up” is a verb phrase or idiomatic expression that is seldom used in the English language. “Hold up” can represent different meanings depending on their usage in sentences. The basic meaning that this phrase depicts when used as an idiomatic expression in a sentence is “to delay” or “to wait.”
In its basic verb form, it can mean “to lift” or “to support.” For example, hold up that chair while I fix this under it. It can also mean “to withstand,” “to fulfill,” “to detain.” In contrast, “hold on” is also a verb or idiomatic expression that is more popularly used than “hold up.”
Basically, “hold on” can mean “to wait for a short while,” “to keep,” “to grip or grasp firmly,” to store,” or “to be persistent.” Example for this expression is: hold on to a bit while I get you the drink. Another one says “hold on to the ball to prevent it from falling.”