I assume this is a 8 bar idea that repeats after bar 8.
"Function" is a loaded word in music theory. The is formal harmonic function which is essentially a framework of harmonic progression moving through categorical types of chords, chord functions: pre-dominant, dominant, tonic. Sometimes chord symbols with Roman numerals are used to represent the chords like
ii6 V7 I.
Let's skip over some analysis and just point out that your chord progression does not use those functional categories. Not a problem, we just look at the chords in other ways. You could analyze dissonance and consonance and chord qualities (like major versus minor.) You could also analyze linear aspects and voice leading.
The first thing I noticed was all your chord roots move by step. That's very linear. The line goes down two steps then back up making a smooth undulation.
Second I noticed that almost all the chords are the same quality. They are all
maj7. Diatonic chords don't do that, so this is chromatic harmony. I think
maj7 chord have a bright, pretty sound. They can sound mellow, kind of drifting around without a (functional) goal. If you played this progression with a samba rhythm it will probably sound like Antonio Carlos Jobim! Anyway, your basic palette is bright & colorful, and the feel is potentially laidback.
Am7 at the end is the concern.
Aesthetically you could describe this in endless ways. It's a surprise. It's a question, etc. etc. I think an objective thing you can say is provides a break in harmony that potentially could become too static. Placing it at the end of the progression I think really works. Objectively is demarks the boundaries of the progression. That gives it shape. Aesthetically, is like a someone is daydreaming and suddenly at
Am7 thinks "maybe I will... " and then upon repeating and returning to the original chords they say "...on second thought, maybe I won't." Replace that with any narrative you like. The point is something happens at the end of the progression, but it doesn't take up a new idea, it returns to the opening idea.
From a voice leading perspective something noteworthy happens with
Cmaj7 Bbmaj7 Abmaj7 all involve all the voices moving. (In this context "voices" just mean the tones of the chord.) But with
Am7 two of the voices change -
Eb move up to
A natural and
E natural - but two voices
G don't change between the two chords. Also, that step upward of the root at bars 7 to 8 mirrors the same step upward at bars 3 to 4. The kind of symmetry is another good way to give form to the progression when functional harmony is not determining form.
When the whole progression repeats there is another important thing to point out about the
Am7. It is the relative minor of
C major. Relative major/minor pairs have a sort of shared musical identity. Traditionally the idea is they come from the same key, but when comparing just the chords they share similar tones.
C E G B and
A C E G. They differ by only one tone, three of the tones are shared
C E G.
If we considered this music to be in
Cmaj7 is the tonic and
Am7 is the submediant. There is a certain idea in music theory that the submediant can act as a sort of alternative tonic. I don't think that's really the theory we want to apply, but it does sort of support the idea that
Am7 isn't so strange here. It's a kind of direct link back to
Cmaj7. Regardless of that theory it's easy enough to see that with 3 out of 4 tones shared it's a smooth transition from
I put it in notation to better see some of the voice leading stuff...
...I used ties to show the shared voices. I don't mean to literally hold those tones, the ties are just to show the notes are common tones between chords.
Also, with the first chord change I had the top voices move in the opposite direction of the bass. I did that to set up a smooth step-wise move back from
Cmaj7. Blue arrows highlight that motion. You don't have to do that, but it is common to arrange the voice leading my smooth steps this way when the chords move chromatically through non-functional chords.