What does a girl mean when she wants to take things slow?

For instance, it can refer to someones desire to hold off for a certain amount of time before engaging in different kinds of intimate acts, while in other circumstances it can simply mean that someone wants to wait before making a serious commitment.

Why does a girl want to take it slow?

The answer is that in many cases, taking it slow is a positive sign that someone sees the potential for a long term relationship with you. After all, it takes effort to maintain any relationship. If they werent in the least bit interested, theyd probably make that pretty clear one way or another.