At the molecular level

Thin filaments are composed of molecules of actin ; thick filaments are composed of molecules of myosin and have a "head" attachment which can bind to the thin actin filaments when provided with enough energy (ATP).

The myosin thick filaments essentially 'walk' along the actin thin filaments, using their "heads" as feet, which form cross-bridge bonds on contact with the actin filament.

Adapted from Campbell, N. and Reece, J.  Biology. International 7th Ed. San Francisco: Benjamin Cummings, 2005, p. 1066-1069.