In most songs there is an underlying harmonic pattern consisting of one chord moving to another and eventually coming to rest or beginning again on the first chord of the key. This chordal movement can be seen in most chord progression.
If you look at a simple chord progression in the key of C major, it is easy to see how the system of Roman numerals works. The following example contains the chords C, F and G. Since these chords correspond to the first, fourth and fifth degrees of the C major scale, the progression could be described as 1 4 5 1 in the key of C.