It's possible to chip a tooth without noticing. A tiny fragment might have been lost when you bit down too hard on a particularly tough piece of food. If the tooth was already being affected by decay, even biting down on something soft can cause a fragment to detach. The fragment itself would have been tiny and was almost certainly swallowed. In fact, you might be blissfully unaware that your tooth has a new sharp edge until it begins to irritate your tongue or the lining of your cheek. Treatment generally involves the elimination of that sharp edge.
This elimination can be quite literal. When only a tiny fragment of the tooth has chipped away, your dentist will assess whether its loss will compromise the overall tooth, making it more vulnerable. When it's determined that this isn't the case, your dentist can correct your jagged tooth by literally removing the sharp edge, using a process known as dental contouring (also called enamel shaving). The jagged portion of the tooth is shaved off using a small handheld tool, which smooths out the affected area.
Dental contouring is only useful when the missing fragment is very small indeed. When the fragment is large enough to have resulted in significant loss of the tooth's overall structure, it won't be much help to remove even more of the tooth. Your dentist can replace the fragment via dental bonding, which is when a tiny amount of dental resin is applied to the jagged edge and shaped to approximate the missing fragment. Instead of compensating for the lost fragment, it's given an artificial replacement.
An even larger fragment requires yet another approach. You'll likely begin to notice a larger fragment beyond the irritation to the soft tissues inside your mouth. When a large enough tooth fragment is lost, the tooth can become more sensitive to temperature and bite pressure, and the tooth can be vulnerable to an accelerated rate of deterioration. This can warrant a dental crown, which is when sufficient dental enamel is removed to accommodate a porcelain shell (the crown) that is fitted over the tooth to protect it. The crown can be partial or whole, depending on how much coverage is needed.
A jagged tooth can be irritating, and in many cases, this irritation is the worst that will happen. But it can also signal the beginning of a more serious problem for a tooth if the issue is not treated, so it's best to see your dentist soon.