That is mostly correct.

Most cock rings fall into the sex toy catagory and are worn around both the cock and balls. To put this type on, one first puts his balls thru the ring and then the soft cock is pushed thru. Once the cock is erect, the ring cannot be removed until the erection goes down. And it will go down eventually. A cock ring does tend to prolong erections, but it will not keep a cock hard forever.

But, as mickey192 correctly states, the main purpose of this kind of ring is to make a man's equipment more attractive and to make things look bigger. It holds the balls down in the sac and pushes everything forward for a more pronounced appearance when nude. It also makes for a bigger bulge in the crotch of a snug fitting bathing suit or snug fitting pants. What man doesn't want that? I, too, wear mine 24/7.

But there is another kind of cock ring that is a bona fide medical device and that is sometimes prescribed by doctors for ED. A friend on mine had one that was prescribed by his doctor for that very purpose. This kind is worn just around the penis at its base. It is snug fitting and it restricts b-l-o-o-d flow out so that an erection can be maintained.