We sell two kinds of 3-way ball valves: one is an L-port, and one is a T-port. This product page shows the L-port valve. The L and the T in the names refer to the hollows in the ball inside the valve and the resulting shape of the open branches. For example, the L-port valves have two hollows in the ball which results in two branches of the valves being open at right angles to each other, resembling the shape of an L.
There is a handle on top of the valve which allows you to angle the hollows in different directions, meaning you can open and close whichever branches you need - as long as they are next to each other. The design of the L-port means that you can shut the valve off completely, because you can point one hollow to the back of the valve where there is no branch, while the other hollow takes the fluid but doesn't have anywhere to send it. Both of the valves come with unions on each of the branches so that you can quickly and easily remove the valve and service or replace it, without having to cut your pipe.