If something is briny, it's wet and salty, like seawater. You should probably rinse out your briny swimsuit and hang it to dry in the sun.
Salty ocean water is briny, and seafood often tastes a bit briny as well: "I love these briny oysters, but my brother can't stand them." Your brother may also like to keep his feet on the beach while you dive into the briny water. In the 17th century, briny was originally used to describe tears. The Old English root is bryne, "water saturated with salt."