It means to be in a difficult situation without the means to get out of it.
Imagine yourself in a canoe on a creek, but you have no paddle. You're stuck, unable to move forward or steer, making you vulnerable to the current and any obstacles in your path.
Here's an example:
"After losing my job and my apartment, I feel like I'm in a creek without a paddle. I don't know how I'm going to get back on my feet."