Lauter Tun is a vessel for separating the wort from the solids of the mash.
Mashing occurs in a separate mash mixer, in which case the mash must be transferred by a pump to the lauter tun. The mash is usually pumped in from the bottom or side of the vessel to avoid excessive aeration of the mash.
Other brewhouses may have a setup in which a single vessel serves as both the mash and the lauter unit, thus eliminating the need to pump the mash. These systems remain common in the UK for performing single temperature infusion mashes. Such mash tuns, like lauter tuns, are fitted with false bottoms. The advantages of a combination mash/lauter tun are less up-front equipment cost and a smaller footprint in the brewhouse. The advantage of two separate vessels for mashing and lautering is that the mash tun can be filled again with a new batch while the previous batch is still running off into the kettle. Thus, a separate lauter tun allows a brewery to produce more brews per day than would otherwise be possible.
Bibliography
Brewing Trade Review July (1961): 781–2.