My girlfriend reports that a clunking noise can be heard at the rear of the vehicle. It occurs usually when driven over potholes, bumps, squirrels (joking) etc.. I am not really familiar with this type of suspension system.

I replaced the brakes in this car yesterday. When the car was on stands I noticed that I was able to push the driver's side wheel in and out from the top. I mean that when facing this wheel dead on I can push or pull at the top and it will move considerably. This isn't the case with the other wheel.

What is the faulty component here? It's a more elaborate suspension than I'm accustomed to and I'm not really familiar with it as stated earlier.

Thanks for any assistance.

Sounds like the rear wheel bearing/hub is shot. Very easy job to replace.
At RockAuto.com, for a 4 cylinder Accord, a new Timken 512188 wheel bearing/hub assembly costs $75.79:

http://www.rockauto.com/catalog/raframecatalog.php

If it's not the wheel bearing, then there's a suspension problem; e.g. strut, damper mounting bolt, or arm issue.