Cross-bridges in muscles are the small, bridgelike projections from thick (myosin) filaments that reach toward thin (actin) filaments where the two overlap. They attach to actin, pull, detach, and reattach in a repeating cycle that generates the force for contraction.
When ATP is available, that cycling continues; the force of a whole muscle is the sum of forces from millions of cycling cross-bridges. As the filaments slide past each other when a muscle shortens or lengthens, cross-bridges repeatedly change attachment sites.