It's actually a series of games taking place in an alternative future, based around a world running mostly 1950's technology and this world is covered in toxic radiation. In this timeline, robots are quickly developed and put into use.
Robobrain is a robotic body for an organic brain, essentially an extreme form of life extension.
ED-E is a companion of the Eyebot type. It is made to look like an eye with some optic nerves hanging out behind it. It's shape indicates that it's for surveillance.
Yes Man is a Securitron type of law enforcement robot. The difference is that the AI code running in Yes Man is very much modified, so much so that he takes on some of the personality of a stereotypical cowboy.
I recommend looking into Fallout New Vegas as that is the best game in the series. It is where most of the good story/lore is found. Other than that, Fallout 1 and 2 are also good options, but it's only with Fallout 3 that you get 3d graphics. New Vegas came out after and thus has some major improvements.
After New Vegas, Fallout 4 came out and it was a minor disaster because of rushed development and a season pass that only got you about half the value that you should have gotten.
Finally Bethesda decided to try a "fallout online" and named it Fallout 76. It was a complete dumpster fire. It took a long time to get NPCs added as an example. It is okay now but early on, it was pretty horrible because it had been rushed out the door without any consideration of the additional difficulties you get with an online game.
This does not include all of the Fallout games as this post is already very long, but this is the gist of fallout as a franchise.