To 'run out of' something means to finish a supply of something. If you 'run out of' something you need to restock or get another supply. In English, we use this phrasal verb instead of 'finish' when we are talking about things that we buy that have been used. similar in meaning to 'use up'.

1. We've run out of milk, so I'm just going to pop down to the shops and get some more.
2. I have to run out and do a few things in town. Does anyone need anything brought back?
3. Many hospitals are running out of money and urgently need proper financial support from the government.

1. I was worried that I would run out of time to submit my article, but in the end I got it in just before the deadline.
2. I'm running out of patience. You are taking too long to complete this project!
3. I don't think we can continue working on this project. We're running out of money!