A7: the doorway to Dm

From C major to D minor in one harmonic move.

The quick idea

Dm - G - C can be read as ii - V - I in C major. But when you add A7, the route starts pointing toward Dm.

A7 introduces C#, a note outside C major, and adds G, the minor 7th. That extra 7th makes the chord demand resolution with more pressure.

A7 = A - C# - E - G

A major: A - C# - E | A7: A - C# - E - G

The 7th (G) is not decoration. It is the note that makes the chord demand resolution.

Dm = ii
G = V
C = I
A7 = dominant of Dm

Dm = i
Gm = iv
C = VII
F = III