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.
Download the premium PDFWhy A7 has more pull than A
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.
Before / In C major
Dm = ii
G = V
C = I
A7 = dominant of Dm
After / In Dm
Dm = i
Gm = iv
C = VII
F = III