Basically it consists of up to 62.2 separate speaker feeds at the theatre rather than conventional cinema speaker systems for 5.1 or 7.1 This provides enhanced ambience in the auditor, both on the horizontal, and especially vertical, e.g. it'll actually sound like rain, or plane/helicopters overhead.
All 64 channels are much more versatile and can all be individually mixed, unlike conventional cinema with 5.1 or 7.1 speaker systems that are locally grouped (image shown below for comparison), Atmos is a much more realistic and natural sounding experience.
Small auditorium example...