Think of the word convert as meaning "change," whether it is a person who adopts a new belief, or a changing action, such as when you convert dollars into euros.
Many times we can catch a word's meaning by looking at its origins. In this case, the Latin con means "around," while vertere means "turn." So we can figure that convert means to "turn around," an object or one's thoughts on an idea. For example, you might convert a meat eater into a vegetarian or an empty-nester might convert the kids' bedroom into an exercise room.