An entailment is a deduction or implication, that is, something that follows logically from or is implied by something else.
In logic, an entailment is the relationship between sentences whereby one sentence will be true if all the others are also true. Want a less-dry-sounding, real-life example? How about this: Being a good student, for instance, is an entailment of attending classes, learning the material, and keeping up with assignments. An old-fashioned definition of entailment is a set of limitations that restrict the ways property can be bequeathed to heirs.