Explain Taylor's Theorem?

Taylor's Theorem involves two points, x and c, on an open interval. I can't find a clear answer in any of my texts as to what c is supposed to be. My best guess is that to use the theorem to estimate f(x) you have to first know the value of f(c) as an initial condition. Otherwise, I can't see any way to find f(c) in the first place, if what we are doing is trying to find an approximation for the function f. Is this right, or am I screwed up?