“Enure” (or “inure”) means to take effect and serve to the use, benefit, or advantage of a person. “Enure” is commonly seen in formal legal language, though “inure” is more commonly seen in conversation.
A contract that states that something will "inure to the benefit of Bill Smith" means that Bill Smith will receive the benefit of that thing.
For example, in a Residential Lease, if a clause says “This Lease inures to the benefit of the respective heirs, executors, and assigns of each party”, that means that if the owner of the rental property were to pass away, the person who is assigned the lease would be entitled to receive rental payments. The benefit of receiving rental payments would inure to the person who inherits the property.