Here's a photo of my tractor setup that illustrates the problem. You can see the 3 point links that have an implement on them in this photo. You can also see the backhoe mounting brackets (that have 4 mounting points, 3 visible in this shot). Obviously, the backhoe fits in the same place on the tractor as a rear implement hooks up. I'd just ditto my earlier comment about removing the 3 point arms. It's not that big of a deal.
The backhoe mounting brackets are part of the backhoe subframe, which extends underneath the tractor (see photo in earler post). On this tractor, the subframe is permanently mounted to the tractor. Other backhoe designs have a removable subframe, which comes off when the backhoe is removed (see Dave1949's comment).
A subframe mount gives a much stronger support for the backhoe than would be possible using the 3 point links, and a well designed subframe limits how much stress is put on the tractor itself when the backhoe digs. There are many threads on TBN about 3 point backhoes... get a pint of your favorite beverage and enjoy some extensive reading on the subject. Generally, the 3 pt ones are OK for occasional or mild use and not the best for heavy work.
As for the "easy to install" thing, well that's a relative statement. Remember you'll be putting something on your tractor that probably weighs about 2,000 lbs., and it has to be secure so it's safe to use. You're going to go over it with the grease gun (mine has about 30 grease points!), and hook up the hydraulics. It's not difficult, but it does take a bit of time and practice. Interestingly, I've heard that the 3 point backhoes are more difficult to attach and remove than the subframe ones.