The client class represents any client that is connected to the server. Therefore, clients are created and destroyed automatically by players' connections or disconnections. They usually are the MTA: SA copy that a player is using (so it has more information about the world), but it can also be the server console.
All client-managing functions operate on both player and server console elements, so the element responsible for a kick can be the server console, for example. However, the server console is protected against some of that functions: it can't get kicked or banned.
The players' clients are also responsible of informing the server about the state of the elements that they're syncing, so they're essential for accurate sync of peds and vehicles. They also receive data from other clients and the server.