If you describe something as partial, you're usually saying it's just part of the whole, or incomplete. Say someone asks how you started your band and you say, "I bought a guitar." That would be a partial answer, at best.
Partial has another meaning, too. If you say you are partial to something, you are expressing a fondness for it. Or not. If someone asks you whether you still love your husband after 50 years of marriage, for example, and you say, "I'm partial to him," you're either joking or politely saying "Not really." Being partial to something is to love as a warm stove is to a bonfire.