"Resolution" has a slightly broader definition than just "from dissonance to consonance." Before I get to that, though, I want to touch on why exactly that definition is used.
First, let's throw out the chord progression you supplied: it's very 60's doo-wop, and not a good example for common practice harmony. Let's replace it with
|: C F C G :| C (I am using
|: - :| to indicate repeats.)
We are playing in the key of C major. This is clear from the fact that we start and end on that chord, and all of the other chords contain notes within the key of C major. This means that our C chord is called the tonic chord. It functions as a "home base," if you will. In common practice harmony, a dominant chord is one that implies a following resolution to a tonic chord. There are many other names for different chord functions in a key, including mediant, sub-mediant, sub-dominant. I am only going to focus on dominant and tonic here, so you should know that we use
I (Roman numeral one) to refer to the tonic chord built on the root note of the key (C), and
V (Roman numeral five) to refer to the dominant chord built on the 5th note of the key (G).
Back to our progression. Let's change it once more, to
|: C F C G7 :| C. With Roman numerals, we would use
|: I IV I V7 :| I. This is where we get the dissonance that your original definition was talking about. The
V7 chord is called a dominant 7th, because it contains a tritone that strongly implies a resolution to the tonic chord. (The dissonant tritone is caused by the 7th chord member, in this case, F.)
To exemplify this, play G7 as follows: G - F - B (from the bottom of the chord to the top). The F with the B above forms a dissonant interval of a tritone. It should sound odd and unstable. To resolve this chord to our consonant tonic chord of C, move the B up half a step, move the F down half a step, and move the G down a 5th to C. We are resolving the dissonant tritone outward by half-step to our consonant tonic chord.
So, that's essentially where your resolution definition is coming from. Now, let's bring it back to your original example step-by-step.
If we consider
G - C in C major (
V - I), we don't have a dominant 7th chord to fuel our resolution, but it really isn't necessary. If the entire piece has been in C major this whole time, the listener is going to expect the piece to end on the tonic I chord. We call this ending a cadence, essentially meaning a kind of chord-to-chord resolution. The
V chord (G) still has dominant function in the key of C major, so we can say we are resolving to C, EVEN THOUGH the G chord IN ISOLATION sounds like it doesn't need to go anywhere. Context is incredibly important in music theory and analysis.
Now, back to our original example of
|: C F G F :| C, or
|: I IV V IV :| I. The cadence we are analyzing is
IV - I, or F - C. We are still in the key of C major, so the ear is going to expect the piece to end on the
I chord, C. We can call it a resolution from F to C because the ear expects this in context. The
IV - I chord progression actually has a special name: the "Plagal cadence". It is easily remembered since it is commonly used to set the text "A-men" at the end of hymns.
As slim alluded to, a better definition for "resolution" might be a "release of musical tension". Dissonance causes musical tension, as does moving away from the tonic "home" chords. The tension is then released by resolving back to the tonic.