Moving counter-clockwise around the circle of fifths is a study in dominant-tonic relationships.
Download/view a piano reduction of the music from the above video.
In the context of a specific tonal center and the subsequent assignment of harmonic functions, all energy becomes focused on resolving to the tonic (I). The dominant chord (V7) has the specific task of resolving to the tonic with a perfect cadence, but the illusion of a perfect cadence to chords other than the tonic can also be created through the use of secondary dominants.
The secondary dominant provides a temporary resolution (or tonicization) to a chord other than the tonic. It requires a brief alteration from the home key but differs from a key change in that its tendency is still toward reaching the tonic; a key change requires establishing a dominant and subdominant in relation to a new tonic.
In the above video, secondary dominants are shown in the key of C. The progression moves further from the tonic after each resolution, then walks back through each note of the circle of fifths. For example, when the target is the vi chord, the secondary dominant is created by altering the iii to become a III7. Although referring to it as the III7 is not incorrect, calling it the V7/vi (the five-seven of six or the five of six) helps to clarify the function.
A Theory of Music 