A set of formulas is said to be satisfiable if there exists an interpretations (model) that makes all the formulas in the set true simultaneously.
Relation with Consistency
Logical consistency is the property that there is no proof of contradiction from these formulas.
Note that consistency is defined syntactically, which is different from satisfiability, which is a semantic property. In propositional logic and first-order logic, the two notions are equivalent because the logic is sound and complete. But for other logics, this may not be the case. 1