The high explosive surrounding the fissile material is ignited.
A compressional shock wave begins to move inward. The shock wave moves faster than the speed of sound and creates a large increase in pressure. The shock wave impinges on all points on the surface of the sphere of the fissile material in the bomb core at the same instant. This starts the compression process.
As the core density increases, the mass becomes critical, and then supercritical (where the chain reactions grows exponentially).
Now the initiator is released, producing many neutrons, so that many early generations are bypassed.
The chain reaction continues until the energy generated inside the bomb becomes so great that the internal pressure due to the energy of the fission fragments exceed the implosion pressure due to the shock wave.
As the bomb disassembles, the energy released in the fission process is transferred to the surroundings.