Air Pruning is used to make pot plants grow and develop a compact, dense and healthy root system that planting causes minimal damage when planting. (Root) air pruning is sometimes also called root training or root making.

Plants strive for a balance between underground and aboveground part. Roots grow in the direction of the force of gravity. A plant uses its roots to absorb nutrients, and especially water, and to anchor itself. The tiny root hairs (rhizoids) usually live only three days, so they are constantly renewed. The roots extend only in and to damp and nutrient-rich places.

When your plants (from seeds, cuttings ..) grow in pots they need regularly a transplant into a larger pot by the increase of the root system.
Usually this pot period is just temporarily, to keep weak and young plants in a protected and well controllable environment to grow up. Much longer the plant is in a pot, the more the roots went looking for food and moisture. The barrier of the sidewall makes the roots go bow, nod, spiral around growing against the wall. Those root forms are not good for the plant, especially because this process after planting often continues. Also through the drainage holes of the bottom come roots. This breaks many roots down while removing the pot and transplanting.

Air Pruning helps avoid these problems so that you can transplant a plant with a healthy and undamaged root system. For this purpose special pot forms may be used. The side (and bottom) is not smooth, but ribbed (or blocked), and perforated with relatively large holes. Watering is done only from above, by pouring or drip irrigation. So the soil at to outer edges of the pot stays airy and dry, and therefore unattractive to the roots. Which therefore do not grow outward, but inward. The airy wall dries out the root tips, causing no further growth but making them branching. This creates a compact root ball, which also easily can be removedfrom the pot without roots breaking down.

Even with coir fiber, jute, linen and felted bags you get a similar result. With plants that spend their lives in a container aboveground, proceeds with this system would be much better with a healthier root growth that can absorb more nutrients and moisture and wastes less energy on the futile round growth of roots. (Here, the bottom may be kept moist eg. in a bowl.)
You also recognizes the principles at the thatched, willow or heath braided ornamental plant baskets to hang on the wall.

Nurseries use the principle increasingly in containers for trees and shrubs, because they do not know in advance how long their plant material has to wait for a buyer before it will be put into the ground.