A7 means A dominant 7. The notes are A, C sharp, E, and G. The first picture looks like A major with one finger left off. The list says which string that is.
x means muted. 0 means open.
Short code x02020, thickest string first.
A dominant 7 uses the notes A, E, G and C sharp.
More A guitar chords.
Also A major, A minor, A major 7, A minor 7, A suspended 2, A suspended 4, A power chord, A diminished, A augmented.
Short code x02223, thickest string first.
Barre fret 2 with the index finger on the D, G and B strings.
A dominant 7 uses the notes A, E, C sharp and G.
Both pictures are A, C sharp, E, and G. That is A dominant 7. The first picture mutes the thick string, has no barre, and rings three open strings. The second picture bars fret 2. Same four notes. The barre shape usually sounds thicker.
If the A dominant 7 in a song sounds thicker than the first picture, try the barre picture lower on this page.
G is the extra note. It is not in A major. On the first picture that G is the open G string. Play A major after this and that G is gone. The extra note is why this chord wants to go to D major.
Play each line in order.
This is the blues one. A dominant 7 (A7) to D dominant 7 (D7) to E dominant 7 (E7) and home, and it never quite sits still. 1950s Chicago, a back porch after dinner, early rock and roll on the radio. Hungry, not sad. That is why you play it again.
A7 goes to D7 and comes back. Then E7 makes you wait. Slow blues. A kitchen at night, the radio low. The feeling is the wait.
G dominant 7 (G7) walks off, D7 walks you back, A7 is home and still buzzing. 1970s rock, car radio, windows down. Bar-band loud. Not a hymn.