adizero as far as i can tell is a fit system that allows minimal weight while still maintaining necessary support and stability. the shoes have a contoured fit with very thin uppers supported by strapping systems or thermoplastic lines that form something like a ribcage on the inside of the shoes.
as far as i can tell its basically adidas's version of flywire, but the uppers are thinner and the underlying supports are much more substantial.
most of the shoes you see marked with adizero are the lightweight shoes that adidas is pushing for each sport. many of the higher end shoes also have reduced midsoles and redesigned outsoles to reduce weight as much as possible.