First, let's get you familiar with the concept:
TL;DR: Time travel project.
If you dig into what people are saying (stories, reports, etc.), you'll find that there's tie in with the Philadelphia Experiment. You know, make the navy ship disappear and show up in Norfolk, Virginia before popping back.
Anyway, get a little deep into Montauk and you will find that the Philadelphia Experiment was the cause for the Montauk Project (I'm abbreviating that MP going forward). That some of the people who disappeared reappeared in the middle of the MP thus justifying the creation of the project and convincing the US government that this was a worthy project. Digging really deep, you find what are supposed to be an account of someone who worked on the project describing a cylinder or "tunnel like" device that sends you through time. Enough sciency sounding stuff is presented to make people who have an inkling of physics and quantum stuff to scratch their heads and wonder. The same sciency stuff makes normal people think it sounds 100% reasonable.
Anyway, if you ever watched Stargate SG1, eventually they have this alien dude (Martin Lloyd) who is stranded on earth and mostly doesn't remember who he is but makes these outlandish shows called "Wormhole X-Treme!" It's a brilliant parody where Martin is supposed to be a caricaturization of Ira Behr (Star Trek producer, screen writer). The one single statement that lets this hilarious train wreck of story writing happen is that it's an opportunity of "plausible deniability" for the Stargate program. If anyone thinks they know anything about the Stargate Project, the military and government points at this "Wormhole X-Treme" show and paints the person as a crackpot. This is actually a real thing that's done, by the way. The military working with TV and movie shows to create media for the public is quite common. Top Gun is an excellent example of Navy enlistment propaganda.
Enter a real television show called The Time Tunnel. Released in 1966, just a few years after Project Montauk is supposed to start working, it features a device with a "tunnel" that people walk through to travel through time. It ran for only one season and was extremely peculiar in that it's concepts and ideas are not standard fair for any television show. Hard sci-fi attempts to create fictional technology rooted in real physics and then extends it to create its own thing. The Time Tunnel uses real physics and ideas to create a supposedly fictional device but the science isn't fantastical, only the device. It has more strangeness than just that. For example, the story takes place only two years in the future of when the show was produce. No science fiction show does that because of the problems of how to represent high-tech fiction in the real world and alternate history shows was not a genre or even thought of at the time.
Anyway, go dig around and read up some of what I'm talking about here.