It would take all day to go into all the details (that we know so far) about the olefin metathesis reaction mechanism. There have been a number of intense experimental and computational studies on various catalyst systems, and there’s still more work to be done to figure it all out. But the basics are widely accepted and relatively simple to understand.
The two key intermediates in the catalytic cycle are a metal carbene (a compound with a metal-carbon double bond, see I and III below) and a metallocyclobutane (II and IV). The exact detail of how the carbene gets to the metallocyclobutane and back is still up for debate, but the general pathway is universally accepted.
Below is a catalytic cycle for the self-metathesis of propene to give 2-butene and ethylene. The starting point for the catalytic cycle is metal carbene I. This reacts with propene to give metallocyclobutane intermediate II. This four-membered ring then fragments in the opposite direction to release ethylene and create a new metal carbene III, which reacts with another equivalent of propene. Fragmentation of the resulting metallocyclobutane IV produces 2-butene and regenerates the initial metal carbene which re-enters the catalytic cycle.