A belief is simply anything we mentally or intellectually accept as true. For example, we believe and accept as true the nature of the Godhead as taught by the Prophet Joseph Smith. We believe and accept as true the restoration of the gospel in its fullness in these latter days. And, most importantly, we believe and accept as true the reality of the atoning sacrifice of the Redeemer. In summary then, belief is the mental and intellectual acknowledgment, acceptance, and assent that something is true.
Belief requires only the mind.
Faith grows out of and builds upon belief and produces action. Faith is not merely a positive mental attitude, or a strong will, or a Pollyanna-like approach to significant personal and public problems. Faith is evidenced in deeds. And as faith is the principle of action, so the opposite of faith, which we typically refer to as doubt, is the principle of inaction. Thus, if you and I have faith in Christ, we accept and live His teachings and we accept and obey His commandments.