Air-pots have many benefits. For one, they help promote horizontal root growth through air-pruning of the roots. Because the walls have holes that expose the roots to light, the roots don't become rootbound as they would in a regular container.
The roots don't bind up in the Air-Pot so the plant can later be transplanted outdoors and adapt to the soil more quickly and with greater vigor.
Another benefit of the Air-Pot it it's re-usable and unlike fabric pots they don't retain salts from feeding the plant nutrients. The containers are pretty easy to store, they unwrap to be stowed away somewhere in a shed or closet space.