"Soaking wet" is a common phrase that means that something is very wet:

When he got home from the game, his shirt was soaking wet with sweat.

You can also say that a person is "soaking wet":

By the time I got to the interview, I was soaking wet.

To "soak" means to become filled with water, so this phrase is an exaggeration that compares the wet person to a sponge or something that's completely full of water.