The Watcher Base is a Watcher arms manufacturing plant that manufactures tanks and other weapons for the Fascist war effort on Earth.
Will Grey is taken here after the Watchers infiltrate The Ark, kill Nikola Tesla, and knock him out in the third Episode of the game. The reason he is taken here are unknown, but it may be due to the fact that the Base also doubles as a prison/brainwashing facility, due to the fact that there is a video playing of an Elder explaining how humans should be subordinate to the Watchers. This is unconfirmed though.
Eventually, Atem and several other Survivors come to rescue Will from the facility. Whilst being rescued, Will is told by Atem of the nature of the Watcher conspiracy on Earth, and that the Survivors were prepared for the Watchers to infiltrate The Ark, if they ever did.
After escaping from the base, it is revealed that The Ark was taken to the base as well (probably for dismantling); however, it is also shown that the Survivors managed to take it back, and they will now use it to close the Watchers' gateway to Earth.