The Nintendo eShop is an online service by Nintendo. It offers downloads for Nintendo 3DS games as well as 3DSWare. It also contains various trailers and other information about a large amount of games by Nintendo. The service is available on the Nintendo Wii U with similar content as well.
All Professor Layton games for the Nintendo 3DS can be downloaded from the 3DS eShop. Once a title has been downloaded, it can be downloaded again at any time free of charge.
To buy something from the eShop, funds need to be added to the eShop account. This can be done through a credit card, or by buying a prepaid card in one of the supported retailers.