1. To remain at some location. Please stay at the train station—I'll come pick you up. Tom's going to stay at the London office and make sure everything keeps running smoothly there.

2. To reside temporarily in some accommodation or lodging. I hate staying at these dingy motels, but it's all I can afford at the moment. They're staying at my sister's apartment while they're in town.

3. To continue trying to do or achieve something, especially after initial failures or setbacks. Often used an imperative, especially in the phrase "stay at it." If you really want to become a comic book artist, you have to stay at it! You can't just give up after your first rejection. I'm really motivated to stay at the writing now that I've had a bit of positive feedback.