If something (reaction or process) lowers the free energy, we say such a process is "spontaneous." That simply means it will tend to happen - much like a ball tends to roll downhill. The reverse of this situation is also evident - if a process is "not spontaneous," then it will tend to not happen. This isn't to say that non-spontaneous processes/reactions never happen, it is just that if they are to happen, some external amount of work must be applied to make the process happen - much like physically taking the ball up the hill to a higher position (the ball will never do this without the aid of applied work).
So when we say "it will never happen" for a non-spontaneous process. What we mean is it will "never happen in isolation." If you can combine this process with another one that is spontaneous, then you can make the total or net process spontaneous.
In chemistry, we are often looking at reactions. For these, we compare the pure products and the pure reactants (in their standard state). This comparison gives us the standard change in free energy for a reaction. If this standard free energy change is negative at a given temperature then we would call it "spontaneous." If it is positive, then it is not spontaneous (the reverse reaction is spontaneous). The standard change tells us about the spontaneity of going from all reactants to all products. However, in the real world reactions "end" somewhere in between these two extremes. This is an important concept called chemical equilibrium. Therefore, we say for reactions that are spontaneous (\(-\Delta G\)) "favor the products" side of the equation; those that are not spontaneous (\(+\Delta G\)) "favor the reactants."