Am B7 Em A7 Am D C
The Am-B7-Em is a modulation from G to its relative minor Em. Am-B7-Em is just the IV-V-I cadence in the Em key.
The Em A7 Am is a little deception. We expect to hear something like Em A7 Dm (a II-V-I of the Dm key, but we don't get the Dm).
I'm hearing the Em A7 as a II-V7 which does not resolve, similarly to a hanging V at the end of a turnaround, and then the Am D C is a new idea. I'm also sensing the possibility that the Am A7 D C may be a temporary shift into an A tonality where we have a bluesy parallel A mixolydian/A dorian mood going on. The overlay of the A7 and Am helps to stabilize the idea that the root note is now A. If this was an instrumental break, the soloist might use these modes. Of course Am D and C also belong to G major, of which A dorian is a mode, so it can transition to rest of the tune more or less smoothly.
It all has to be heard in context to confirm these hunches, of course.
Update after hearing audio:
The A7 here is common device used over minor keys: an alteration of IVm to IV7 (in this case still in the key of Em) It brings in the dorian mode over the minor key and is also part of a common device involving the chromatic notes V V# VI above the root. (To hear this, sing the notes B, C, C#, C, B while playing the chords Em, C, A7, C, Em.
My first interpretation was closer that the A7 ends a phrase, and the Am starts something new. It appears that Am D C is just a II-V-IV in the key of G. There seems to be a longing for the plagal cadence IV-I, but the I never sounds. Where the big rest occurs at 0:26, my brain hears a resolution to a G which isn't there.