Stein manifolds are defined here: http://en.wikipedia.org/wiki/Stein_manifold#Definition
Obviously, M is Stein implies that there is a non-constant holomorphic function defined in it. Is the converse true? I mean, if there is at least one non-constant function over a manifold M, then it is Stein (given that it is Holomorphically Convex)?
If not, can someone point me a counter example?
No, take $M = \bar{\Bbb C} \times {\Bbb C}$. Then $M$ admits non-constant holomorphic functions, e.g. $f(z,w)=w$, is holomorphically convex, but doesn't separate points since every holomorphic function on $M$ is constant in the $z$-variable.