The Crown isn't really the monarchy when used in this sense and it doesn't have much to do with titles and such. It's a synecdoche used to refer to the UK government (and the governments of some commonwealth countries). Crown Copyright is the copyright the government holds in the material it creates. In this case, the Ordnance Survey, which is a UK government agency.

Whether you have to respect that copyright is a different matter, although it may be unwise to use Ordnance Survey mapping data for commercial purposes without a license.