Liquidmanure tank. Please note that in the build mode (SHIFT-P) menu "liquidmanure tank" has nothing to do with cows or pigs, it is not related to cow or pig barns. Liquidmanure tank is simply what the name says, a standalone tank to store slurry, it does not need any other buildings or does it help cow or pig barns in any way, its simply a standalone tank.
HOWTO empty cow barn slurry tank. You need a liquid transport tanker trailer, slurry tanker. Drive to the unloading incon (kind of like a big U with arrow pointing from top down in middle of it, heh), then just hit R to "Start Refilling" as shown in F1 menu.