A high modulus is a stiff rock. A sonic log gives a dynamic modulus from the velocities and the bulk density. A core test that loads the plug gives a static modulus. The dynamic value is higher. Fracture models and wellbore-stability models are usually built on a static modulus, sometimes converted from the sonic log.
The unit is psi or gigapascals. Stiffness affects how wide a hydraulic fracture opens for a given net pressure: a stiffer rock opens a narrower fracture, which changes how far proppant can travel. A modulus from a log that was not corrected for gas or for a bad density reading will be the wrong stiffness.