A stripping basket is either a manufactured item or a home made affair made of a dish pan. It is strapped to your waste on the line hand side of your body. As you strip in line from your cast, it collects and holds the line so it does not get tangled up and ruin your next cast.
We saltwater fishermen use it in the surf or flats to keep the line from blowing or drifting away. You can us it on a boat if you like although most people just strip the line on the deck. A few inland trout fishermen are now using them but not many. It really is a necessity in the salt water. Do a site search on stripping basket or look at pics from the spring clave. You will see the baskets strapped to the waists of wading clavers