Frankenrazor is a term used in the shaving community to describe a razor that is made up of bits from one razor and bits from another razor, so what you end up with is a composite of the razors it was made up from. Making a frankenrazor is easy because most three part razor handles can be interchanged, so you would have the upper and lower parts of the head taken from one razor and the handle from a different razor.
As you can see from the photographs I have an excellent Feather Portable razor from Japan, however the Feather handle, on the extreme right, is a bit too small and weedy. The razor works much better with the excellent Lux stainless steel handle from Poland fitted to it. But were I to want to I could instead use the Lord handle from Egypt on the left, the Edwin Jagger DE89L handle next to it or the Gillette Tech aluminium handle to the right of the razor. They all fit and each one completely changes the balance and feel of the whole razor. If you want to further customise your razor you could have a handle custom made by someone like iKon.
So far so good, mixing and matching can make a better razor. The problem comes when people do this with valuable vintage razors. And they do. If someone has an early Gillette model with a damaged head and a different model with a damaged handle they can put the undamaged bits together to make a frankenrazor. These come up on eBay and as the real thing could be worth hundreds of dollars you can see that this has the potential to be a profitable scam. So take care, if you are buying an old razor first check it out against the photographs on Mr Razor.