To run out of something is to use the last of it. There was some, and now there is none.
It is the full form of run out, and the thing exhausted goes after of, so running out of milk, money, time or patience. Those four are the commonest by a long way. The phrase always describes a supply that has been consumed rather than one that was never there. Running low on something is the warning stage before it, and that phrase is worth having too.
1phraserun out ofTo have no more of something left.
“We will run out of paper before the end of the week.”