Engineered wood is made of layers to provide better stability; a backing veneer, core layer (can be plywood, hevea or HDF) and face layer of solid wood; it is this top layer that gives the impression of a solid wood floor. It can also be used with underfloor heating (bonus). You then have the choice of a lacquered or oiled finish, the benefits of each I am about to talk about, latter being slightly more traditional in appearance.
As it sounds, when you talk about a solid wood floor it means that it is pure wood all the way through, definitely the most expensive, but oh so beautiful. The look is (as you would expect) a warm and characterful floor that shows the history of the tree. Popular choices are Oak, Maple and Walnut. My one piece of advice is that you have a ’shoes off’ policy as the surface can dent fairly easily.