This is an expression that all ESL students should know or learn as soon as possible because it's extremely common. To run out of something or to be out of something means there is none left of something. Something can be sugar, bread, time, money, patience, anything. So if you say, "We ran out of sugar," it means you don't have anymore sugar. When you're on vacation, and you have to go home early, it's usually because you are out of money or you ran out of money.
When you use the present progressive of this phrase, it means you still have some, but it's almost gone. So if you're running out of time during an exam, it means you still have time but perhaps not enough because it's almost up.
A: Hey John, could you run to the store and get some milk? We're almost out of it.
B: Sure. I think we're running out of rice, too, right?
A: Oh yeah. You're right. Could you get some?
B: What are kids doing up there?
A: I don't know. They've been fighting all day. I'm really running out of patience. If they don't stop soon, I'm going to take away their cell phones.
B: I'm going to take one of them to the store with me. That should give you some peace and quiet for a little while.
A: That would be great. Thanks.
time's up - no more time left (for example, at the end of an exam)
That's it folks. Any questions, feel free to comment or send us an email.