1. She wants to get closer to you. Slow dancing is a close, intimate activity, so if she asks you to slow dance, she may be trying to signal that she wants to be closer to you physically and emotionally.
2. She wants to see if you're interested in her. By asking you to slow dance, she may be trying to gauge your interest in her and see if you reciprocate her feelings. If you accept her invitation, it will show her that you are also interested in her.
3. She simply enjoys dancing with you. Regardless of her feelings for you, she may simply enjoy dancing with you and want to share a moment of connection.
Ultimately, the best way to know for sure what a girl means when she asks you to slow dance is to ask her directly. If you're not comfortable doing that, you can pay attention to her body language and other cues to get a better understanding of her intentions.