A secondary dominant is a dominant 7 chord that resolves to a chord OTHER than the I. It briefly treats that chord as a temporary tonic. Notation: 'V/X' = the V of X. So V/V is the V of the V chord.

Most common secondary dominants in major

• V/ii — resolves to ii (e.g., A7 → Dm in C)
• V/iii — resolves to iii (e.g., B7 → Em in C)
• V/IV — resolves to IV (e.g., C7 → F in C, the 'I7' trick)
• V/V — resolves to V (e.g., D7 → G in C)
• V/vi — resolves to vi (e.g., E7 → Am in C)

Why they work

Each secondary dominant temporarily 'borrows' the V→I cadence and applies it to a non-tonic chord. The ear hears the cadence and feels resolution, even though the resolution isn't to the actual tonic. The song gets richer without losing its key center.