"Soaking wet" is a common phrase that means that someone is very wet, usually because of rain or the weather.
To "soak" means to become completely filled with water like a sponge. So when you say that you or your clothes are "soaked" or "soaking wet", it's often an exaggeration. For example, if your coworker comes to work after walking in the rain, you can say this:
You're soaking wet!
...even if your coworker is only kind of wet.