The phrase is thought to have originated in the 1800s, when people would keep cats in small cages on their ships to catch mice. If the cage was too small, the cat would not be able to move or swing around.
Here are some examples of how the idiom is used:
* The room was so crowded, there was no room to swing a cat.
* The apartment was so small, we had to get rid of the dining table because there was no room to swing a cat.
* The train was so packed, there was no room to swing a cat.
The phrase no room to swing a cat is a useful way to describe a situation where there is no room to move or do anything.