I find that the Wikipedia article on Photogravure gives a good detailed overview of the subject. An easier to follow and shorter version can be found in this description of the process. Here's the summary of the technique:

1. Contact-print a positive onto a layer of gelatine sensitized in potassium dichromate. This hardens the exposed parts of the gelatine.
2. Transfer the gelatine layer onto a copper plate.
3. Soak this plate in hot water. This will dissolve the unexposed parts of the gelatine.
4. Etch the plate in a ferric chloride. Here the remaining gelatine slows the etching, resulting in smaller wells that will hold less ink in printing.
5. Make prints from the plate.

I have tried to create the following illustration that might help understanding the process:

As you can see, this means that photogravure is a form of intaglio printing, as the image is incised into a surface and the sunken areas hold the ink.

On a sidenote, this article on Photogravure by the Getty Conservation Institute gives some historical background, discusses important variants, and also talks about identification of photogravure prints.

Finally, see also Photoengraving for the more general family of processes related to photogravure.