The Rapid Response Team had a range of functions. During peacetime they were involved in search and rescues, counter-terrorism, disaster relief and special law enforcement. During times of conflict they were tasked with missions behind enemy lines such as reconnaissance, sabotage and deception missions.
During war a Rapid Response Team was roughly equivalent to a platoon in terms of size. A lieutenant usually commanded a team, with around half the members fully trained ensigns and the rest made up of enlisted personnel with years of experience. During peacetime the teams had a different organisation.
On stardate 51614.7, Rapid Response Team 23 under the command of Lieutenant Nosar Drin were involved in the successful Sabotage of Vuldok Nor during the Dominion War. (The Dominion War Sourcebook: The Fires of Armageddon)