Solid hardwood is exactly as it sounds. It is manufactured using one wood species and milled from a single piece of lumber. Although commonly sold in maple, oak, birch, bamboo, pine and other readily available species, solid hardwood can also be found made from more exotic and expensive materials including teak, cherry or even eucalyptus.
The most attractive aspect of solid hardwood is that it can be sanded and re-finished numerous times - extending the useful life of the floor and even giving you the opportunity to change the color. Solid hardwood can be glued directly to the subfloor in certain situations and is available in numerous colors and plank sizes.
Each species is rated for hardness using the Janka Hardness Test. The higher the number, the more resistant the flooring to scratches and dents.
Contrary to what you might hear, engineered wood products are "real wood". The primary difference between an engineered and a solid product is that the former is manufactured with a series of wood layers glued together (similar to plywood.) The top layer or "wear layer" is a hardwood species while the materials below it are often constructed from softwoods.
There is very little difference in appearance between solid and engineered flooring. The latter however has properties that make it a better choice in some situations. For example, engineered floors are more resistant to warping than solid floors and can be laid "below grade" (in basements for example) with the proper subfloor preparation.
The main drawback to an engineered wood floor is that the top layer is comparatively thin. This material can be sanded and refinished in a similar manner to solid wood however often only two or three times before wearing through the top layer. More expensive engineered flooring will have a thicker wear layer which extends the useful life of the material by several years.
Laminate is not wood. Not entirely anyway. Most laminate flooring products are manufactured with a base melamine layer, a thicker fibreboard core, printed decorative layer and a durable top tread layer.
Laminate flooring technology has improved tremendously over the years. Most of these products are more stain and dent resistant than real wood (great for the kids play areas and pets) and the pattern printing process results in unlimited color and grain options. Laminate is less expensive than solid and engineered wood, is lighter, easier to install and more moisture resistant.
The primary drawback to this product is that it cannot be re-finished. Despite manufacturing improvements, most laminate flooring does not have the real wood look or feel and some homeowners still see it as a "cheap" alternative. This is a common conception among home buyers as well so it might be best to consider an alternative if you are renovating to sell.
For more information on wood flooring products, try the National Wood Flooring Association.