In a stateful architecture, the state of the system (i.e., the users data, decisions, etc.) is stored directly on the server. This means if User A leaves the application and returns they must be reassigned to the same server, or else they will lose all their progress / information.
In distributed systems, assigning users to specific servers would cause major overhead in adding / removing servers and negatively impact an application's performance. There is a method for handing this called, [[sticky sessions]], but many applications opt for a [[stateless]] architecture to avoid issues related to state.