What is what does it mean when a girl smiles and waves at you?

When a girl smiles and waves at you, it can convey various meanings depending on the context and your relationship with her. Here are some common interpretations:

1. Friendly Gesture: It could simply be a friendly gesture, indicating that she is acknowledging you in a positive and polite way. It might not mean anything beyond basic civility and goodwill.

2. Recognition: If you know each other, she might be recognizing you and expressing her pleasure at seeing you. It reflects a level of familiarity and acknowledgment.

3. Invitation to Converse: A smile and wave can also be an invitation to start a conversation. It's a non-verbal cue that she is open to interacting with you.

4. Interest or Attraction: In some contexts, especially if coupled with lingering eye contact or a more personal smile, it might indicate interest or attraction. Consider the context and any history you might have.

5. Politeness: Sometimes, a smile and wave are just polite ways of responding when making eye contact with someone, without deeper implications.

The best way to understand such gestures is to consider the context, body language, and any existing relationship you may have. If you're unsure about her intentions and you wish to clarify, engaging in a conversation could provide more insight.