Resolving

Resolving is a way to lead songs back to the tonic or root. It can be applied to single note applications, or it can be applied to chord progressions. If you don't already know, the 7th degree is also called the Leading Note because it leads back to the tonic. The leading note is a half step from the tonic, so when you resolve, you use half steps. In single note applications it is pretty easy because you just have to think to play from one fret down back to the tonic. When you play with chord resolutions it gets a bit more complex.
Whenever a chord progression is being played, you are always trying to resolve back to the tonic. Not every chord resolves directly to the tonic, but they will resolve indirectly. Let me show what chords resolve directly to the tonic.

Chords that Resolve Directly to the Tonic

The chord that resolves to the tonic the best is formed from the 5th (V) degree of the scale. The reason that this chord is the best is because it contains the leading note (7th degree). In the Key of C, B is the leading note because it is the note before C. Look at the chart below.

C Major Scale

I II III IV V VI VII Octave
C D E F G A B C

C Major Notes

C E G

G Major Notes (V chord)

G B D
The Dominant Chords formed from the 5th degree resolve better than the plain major chord because the b7 note that is added in dominant chords resolves to the third of the tonic (in this case it is E), and the B is still in the chord to resolve to the C. Look at the chart to see the notes.

C Major Notes

C E G

G7 Notes

G B D F
Because the V chord resolves so nicely to the tonic (I chord), many songs end with this progression because it is such a strong ending for songs.
The diminished 7th chord also resolves nicely to the tonic because it is formed from the leading note (B). In the key of C, the diminished 7 is B diminished 7 which contains the notes B, D, F, Ab. This resolves nicely to the tonic because the B resolves to the C (and Bb if you are playing a C7), the F resolves to the E, and the Ab resolves to the G. Look at the chart below.

C7 Notes

C E G Bb

B Diminished 7 Notes

B D F Ab
The III chord will also resolve to the tonic. Just remember that it is minor when you play it. It resolves best with just a plain minor chord to a I major chord.

Chords that Resolve Directly to the V

The II chord resolves directly to the V chord (and therefore indirectly to the tonic) because the II chord is the 5th degree from the V. In other words it is the dominant of the dominant. If you took the V chord (G) and wrote out its major scale the 5th degree of that scale (G major scale) is the same as the II chord (in this case it is D). This is where we get the II-V-I Jazz Progression.
The IV chord also resolves nicely to the V chord but not as well as the II chord. This is where we get the chords of the 12 bar blues (I-IV-V).

Other Chordal Resolutions

The VI chord resolves to the II chord because the VI chord is the dominant of the II chord (just like the II is the dominant of the V). Remember that the II and VI chords are minor chords.