Plants grow in different patterns... most of a plant can't grow like an animal, because of the physiology of the cell, plants (with very few exceptions) have cell walls made of cellulose... so it is useful to think of an adult plant cell as a brick... and you can't easily expand a brick structure from the middle.
so plants grow in small regions call "meristems" these are the only places that a plant can grow... and basically any place you see a plant growing (not just expanding) is a meristem. the tips of the roots, buds, and the special meristem that is the main growth bud of a plant is called an "apical meristem"... so that is the background.
Cactii only have a couple of growth patterns, a few like Organ Pipe, and Saguaro, and Barrel Cacti have a main meristem that just keeps growing indeterminately, but many, like Cholla, Easter Cactus, Christmas Cactus, and Prickly Pears will grow to some predetermined size then stop, and for further growth to occur it has to bud and create a new growth area.
This is just how they are, some cactus use this to spread, they can break off and become a new plant where they fall, others just grow this way to accommodate seasonal growth...