Seventh chords add a bluesy, soulful quality to progressions and are extremely common in folk, country, rock, and blues. They are built by adding a flatted seventh (the ♭7) interval to a major chord. Many of these open shapes are simple modifications of the basic open chords you already know.
For example, the A7 chord in open position uses just two fingers — middle on the 2nd fret of the D string and index on the 2nd fret of the B string — leaving the G string open. That open G string naturally provides the ♭7 note (G is the ♭7 of A major), giving the chord its dominant 7th character. The D7 chord uses the same skeleton as D minor but lifts one finger away: index on the 1st fret of the B string, middle on the 2nd fret of the G, and ring on the 2nd fret of the high E. The fretting of the C (1st fret of the B string) provides the ♭7 that defines D7. The E7 chord is essentially an open E major with the ring finger lifted off the D string, allowing the open D note (the ♭7) to ring.
Other open seventh chords use slightly fuller shapes. The G7 chord requires three fingers spread across the neck: index on the 1st fret of the high E, middle on the 2nd fret of the A, and ring on the 3rd fret of the low E; the F note at the 1st fret of the high E serves as the ♭7. The B7 chord is one of the more complex open-position chords, using all four fingers: index on the 1st fret of the D string, middle on the 2nd fret of the A, ring on the 2nd fret of the G, and pinky on the 2nd fret of the high E, strummed from the A string down. Mastering these shapes rounds out the basic open chord vocabulary.