A healthy tooth has a space inside it called the "pulp space" which is filled with soft tissues - nerves, blood vessels and pink connective tissue. It looks kind of like what you'd see underneath your skin if you grazed it. If a tooth gets a large cavity, the bacteria in the decay can damage the pulp, which is often what causes toothache.
With adult teeth, damage to the pulp usually means you have to clean out all the space - including any remaining pulp - and fill it in. This is called Root Canal or Endodontic Therapy. But baby teeth only have to survive until an adult tooth comes through to replace them. They also have a better blood supply, so sometimes the pulp tissue in the canels can be saved.

Primary (baby) teeth

Baby teeth in children have relatively large pulp spaces and a cavity doesn't have to get very large before it reaches the pulp chamber.
When the soft tissue in the pulp chamber is infected (has bacteria in it) or affected (is inflamed), it can be removed by a dentist under local anaesthetic. If the soft tissue in the canals is still healthy enough, a special medicated filling can be put into the chamber in an attempt to keep the remaining pulp (in the canals) alive. The process of removing the pulp from the chamber is the actual "pulpotomy", though the word is often used for the entire process including placement of the medication.
Afterwards the tooth is restored with a regular filling or a stainless steel crown.

Permanent teeth

Pulpotomies are only done in permanent teeth

Permanent teeth

Permanent teeth are the second set of teeth formed in humans. There are thirty-two permanent teeth, consisting of six maxillary and six mandibular molars, four maxillary and four mandibular premolars, two maxillary and two mandibular canines, four maxillary and four mandibular incisors.The first...

 (adult teeth) as a temporary alternative to proper root canal therapy. For example, if there isn't enough time, the patient is travelling or they can't afford to have more conventional treatment.

Partial Pulpotomy for Carious Exposures

In some cases an adult tooth might have decay down to the pulp but the pulp is still pretty healthy. If the roots haven't finished forming yet, a partial pulpectomy might give it a chance to finish forming.

Partial Pulpotomy for Traumatic Exposures (Cvek Pulpotomy)

When a baby tooth or young permanent tooth is traumatised - say, hitting your teeth on the handlbars of a bike - it can be broken in such a way that the pulp is exposed. Again, a partial pulpotomy may help it to finish developing and be saved.

Medicaments can be used in pulpotomy

In primary teeth… medicaments such as 1. formocresol 2. Ferric sulphate 3. Calcium hydroxide

Calcium hydroxide

Calcium hydroxide, traditionally called slaked lime, is an inorganic compound with the chemical formula Ca2. It is a colourless crystal or white powder and is obtained when calcium oxide is mixed, or "slaked" with water. It has many names including hydrated lime, builders lime, slack lime, cal, or...

 can be used in pulpotomy.

Although, clinical and radiographic success rate of ferric sulphate is higher than the other materials.

Electro-surgery pulpotomy

It is known as non chemical devitalization. Its mechanism of action is the cauterization

Cauterization

The medical practice or technique of cauterization is the burning of part of a body to remove or close off a part of it in a process called cautery, which destroys some tissue, in an attempt to mitigate damage, remove an undesired growth, or minimize other potential medical harmful possibilities...

 of the pulp tissue. It carburizes heat denaturated pulp and bacterial contamination.

Laser pulpotomy

This technique overcomes histological effect of electro surgery. It creates superficial zone of coagulation necrosis

Necrosis

Necrosis is the premature death of cells in living tissue. Necrosis is caused by factors external to the cell or tissue, such as infection, toxins, or trauma. This is in contrast to apoptosis, which is a naturally occurring cause of cellular death...

 that remain compatible with underlying tissue& isolate pulp from vigorous effects of the sub-base.

Objectives

1. Maintenance of radicular portion vitality.

2. Clinical and radiographic evaluation should show no complications such as, pain, swelling, internal resorption

Internal resorption

Internal resorption is an unusual condition of a tooth when the dentin and pulpal walls begin to resorb centrally within the root canal. The first evidence of the lesion may be the appearance of a pink-hued area on the crown of the tooth; this condition is referred to as pink tooth of Mummery,...

 or abnormal canal calcification.

3. Neither breakdown of the supporting tissue, nor trauma

Physical trauma

Trauma refers to "a body wound or shock produced by sudden physical injury, as from violence or accident." It can also be described as "a physical wound or injury, such as a fracture or blow." Major trauma can result in secondary complications such as circulatory shock, respiratory failure and death...

to succedaneous teeth should be detected.