The Game client is software which can be downloaded or purchased, and then can be installed on the computer of the player. Once installed, the player can start the client. Often a login with a Battle.net user name and password is required. There will be a communication between the client and the server that stores several data.
From time to time Blizzard makes changes to the servers and to the client. For the players, this means that they have to patch the client to a newer version, which generally happens by means of the Launcher.