Zoom Air is like a little air-filled plastic pillow they insert in the midsole. It's very similar to the Nike Air units they've been using for decades, but the "Zoom Air" unit has little microfibers inside the pillow that apparently help create a springier feel. Zoomx is a kind of foam used in the midsole itself.

Check the fit. When the shoe is on your foot, you should be able to freely wiggle your toes. Make sure you can fit at least one thumb between your longest toe and the end of the shoe's toe box. The shoes should be comfortable as soon as you try them on. Don't plan on them fitting better after "breaking them in."