The structural integrity field is a network of forcefields that reinforces a starship's frame, allowing it to withstand the stresses of acceleration, warp travel and combat.
A starship's physical structure alone could not survive the forces involved in high-speed maneuvers. The structural integrity field adds energy reinforcement throughout the spaceframe, and engineers divert extra power to it when a ship is damaged or pushed beyond its design limits.
Loss of structural integrity is one of the most dangerous situations a crew can face, since a failing field can let a ship tear itself apart. Damage reports aboard Starfleet vessels routinely track the field's status alongside shields and hull breaches.