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You most likely know that the V-I chord progression is the "strongest" in music and that most songs feature it (often at the end of a sequence of chords.)

For example, in the key of C that's G to C and if you look at many songs in the key of C you are likely to find that many of them end with this sequence of chords (it's also known as a "perfect cadence.")

But do you know why this is the case?

To find out you have to break apart each chord to it's elements (the notes within it.) I'm going to continue with the key of C example because using a real world example makes explaining it much easier.

The C chord (the I or "tonic" chord in the key of C) is made up of the notes C, E, & G. The G chord (the V or "dominant" chord in the key of C) is made up of the notes G, B, & D.

The first thing you should note is that they both share the note G. This means that when we hear these two chords one after the other our brain picks up on that note being the same. We don't hear it going from G to C as we might assume.

Then you should notice that the other two notes of a G chord are B and D and that both of these notes want to resolve to the C note. The B note is the "leading tone" of the key of C and it wants to resolve up to C and the D wants to resolve down to C.

This pressure of the B and the D notes both wanting to resolve to C is what makes the G to C chord progression so powerful sounding. It's not because of the note G to going to the note C (a perfect 5th down.) I think that's worth repeating. We don't hear that because both chords have the G note, so we hear that note as going nowhere at all.