A list of tasks, problems, or issues that need to be addressed or dealt with.
The expression is used because laundry is often seen as a tedious and long chore, just like dealing with a lot of tasks can be.
Here are some examples:
* "I have a whole laundry list of things to do before the meeting."
* "The new CEO has a laundry list of problems to solve."
* "After the party, I had a laundry list of things to clean up."
So, when someone says they have a laundry list, it means they have a lot to do.