In Chapter 19 of Feynman's Lectures on Physics, Volume I, it says
...where can we apply a single force to balance the gravitational force on the whole thing, so that the entire object, if it is a rigid body, will not turn? The answer is that this force must go through the center of mass..."
What I don't understand is, what does it mean for the force to "go through the center of mass"? For example, if we are holding up an object, we exert the force on the side of the object instead of its center. But the object does not rotate, so I assume that the gravitational force on it should be balanced. Then, what exactly counts as "going through the center of mass"?
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