Although they have no formal organisation, being named as a templar is a great honour for the Cainite so titled. Being recognised as such a symbol of strength in the Sabbat and a public acknowledgement of one’s fighting skills.
Templars serve a variety of duties, always in a martial capacity. Most archbishops keep a cadre of such cainites in their retinues to handle delicate matters best solved by a judicious application of violence, while the Inquisitors tend to having templars with them as backup for muscle in their travels.
Templars are forbidden from becoming members of the Black Hand, which is seen as a conflict of interests as most of them generally have no secondary factional agendas. However, a Templar can be promoted to the rank of a Paladin.