В отдельном потоке.

Из справки по TIdTCPServer.OnExecute Event
OnExecute receives a TIdContext argument that represents the task for the client connection, and contains a TIdTCPConnection instance for the client connection, and the thread or fiber that controls execution of the task. A protected procedure in the server that triggers OnExecute is assigned to the TIdContext, and eventually the thread or fiber acquired from the Scheduler for the server.


Из справки по TIdTCPServer
TIdTCPServer allows multiple simultaneous client connections, and allocates a separate unit of execution for each client connecting to the server. Each client connection represents a task that is managed by the Scheduler for the server. Listener threads use the Scheduler to create an executable task for each client connection.

The Scheduler handles creation, execution, and termination of tasks for client connections found in Contexts. The ContextClass property indicates the type of executable task created for client connections and added to Contexts.

There are basically two types of Schedulers available for TIdTCPServer: Thread-based and Fiber-based. Each is designed to work with a specific type of executable task that represents the client connections. There are further Scheduler refinements that allow a pool of pre-allocated Threads, or Threads which perform scheduling for dependent Fibers.

The default Scheduler implementation in TIdTCPServer uses a Thread to represent each client connection. Threads are a common feature found on all platforms and Operating Systems hosting the Indy library.