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

It's tricky to definitively know what a girl's wave means without additional context. However, here's a breakdown of possible interpretations:

Friendliness/Politeness: This is the most common reason. She might simply be acknowledging your presence in a friendly and polite manner. She may be waving to a group of people and you are in that group, so make sure to see if there is anyone else near you.
Acknowledgement: Perhaps you've met before, and she's recognizing you. This doesn't necessarily indicate romantic interest, but it means she remembers you.
She Knows You: If you have a mutual friend, or you've seen each other around often, she might be waving as a way of saying "hello" without necessarily wanting to engage in a deeper conversation.
Flirting/Interest: This is the scenario most people hope for, but it's less common than the above. If the wave is accompanied by a smile, eye contact, and other signs of flirting (like <a href="https://www.wikiwhat.page/kavramlar/body%20language">body language</a> that suggests she's comfortable around you), then it could indicate interest. However, don't jump to conclusions based on a single wave.
Mistaken Identity: It is possible she is waving at another person behind you. Check to see if someone she knows is around.
Trying to get your attention: If you have been making prolonged <a href="https://www.wikiwhat.page/kavramlar/eye%20contact">eye contact</a> then she may be trying to signal you.

Important Considerations:

Context is Key: Where are you? What's your relationship to this girl? Has she waved at you before? These details matter.
Her Personality: Is she generally a friendly and outgoing person who waves at everyone? Or is she more reserved?
Don't Overthink It: A wave is a simple gesture. Try not to read too much into it unless there are other supporting signs.

What to do:

Wave Back: If you're unsure of her intentions, simply wave back politely with a smile.
Observe: Pay attention to her behavior the next time you see her. Does she initiate conversation? Does she maintain eye contact? These clues will help you better understand her feelings.
If you're interested, approach her. If you're feeling bold and you're interested in her, use the wave as an opening to say hello. For example, you could say, "Hey, I think I saw you wave earlier. I'm [your name]." But be respectful of her response if she doesn't seem interested.