Thrust is generated by a rotating propeller similar to how lift is produced by a wing.
A region of decreased pressure forms immediately in front of the propeller.
Aerodynamic forces cause the propeller to move into this low-pressure area, generating thrust.
Aircraft Engine Propulsion
The key difference between thrust production in turbojet/turbofan engines versus turboprop engines lies in the mass of air moved and the acceleration imparted to it.
Engine-driven propellers accelerate a large mass of air with a relatively small amount of acceleration.
In contrast, turbojet/turbofan engines accelerate a smaller mass of air with a larger amount of acceleration.