The term sound is most frequently used to describe whether or not an argument is valid and has true premises, thereby guaranteeing the truth of its conclusion. In meta-logic, it is also used to describe a feature of a logical system.
An argument that is sound is one that is both valid, and has all true premises. Therefore, by definition, a sound argument has a true conclusion.
A logical system, or simply a “logic” is said to be sound when anything that can be proven in the system actually follows. That is, if we assume a set of formulas (Γ) and some conclusion (φ), then in a sound system any relationship of provability is accompanied by a relationship of implication.
Formally, a logic is sound if, and only if, when Γ ⊢ φ, then it is also the case that Γ ⊨ φ.
Soundness is an important property of a logical system, because in a system that is not sound, one can prove things that do not actually follow. For example, one could potentially prove a logical fallacy to be valid in that system.