I could delve deep into music theory terms and concepts. I could write long columns about the so-called circle of fifths and how it works and is connected. But let's keep it simple. The circle of fifths is, incidentally, good to have an overview of. If you don't know what the circle of fifths is, I recommend you google it, as it can be of great help in learning chords.
But let's keep it simple, as I said. Chords are connected according to a given, specific system. The C chord is connected to the F chord. Try playing C and F back and forth, and you'll hear it. The C chord is also connected to the G chord (often as G7 in pop and folk songs).
At the same time, the C chord, entirely on its own, is a neutral chord. You can start a song with this chord, and you can end a song with it. The chord you play after a C can be many different ones, without it sounding unnatural.
C7 is not nearly as neutral. Very few songs in pop, rock, and folk music start or end with a 7th chord (septimakkord). What happens when you play a C7 instead is that the pull (or attractive force) from C to F increases. So much so that almost any other chord afterwards sounds unnatural. C7 really wants to go to F. Almost like magnets.
If you want to add some life to a song with few chord changes in C major, you can throw in some 7ths (septimes) (beyond G7 which is probably already there). This is called spicing up chords.
Instead of playing
[C]Tra-la-ta-la [F]Laaa
you can play
[C7]Tra-la-la-la [F]Laaa
You've suddenly brought some life to the song! It doesn't suit all songs equally well. But in many pop, rock, and folk songs, it works perfectly to spice up chords.