The Miller compound is the main locations for meetings and gatherings hosted by May and/or Grace Miller. It serves as a home base for the Miller army.
In Season One, Alyssa mentions the compound when she arrives in Waterfall Creek when she says she just left the compound. Later on in the season, Jared kidnaps Claire. When they're looking for the location, Alyssa mentions that there are plenty of hide-outs from the Millers besides the compound.
In Season Two, we get introduced to the Millers in the compound. We meet May as she is organizing her army. Later on we see Liam reporting back to May about his assignment to kill the Silverstones.
In Season Three, Liam mentions the compound to Mila, saying he'd have taken her there but he would have never had her for himself.
A majority of the Miller army lived there at a certain point. Many vampires had a residence there, including most known Miller vampires