A distress call was any signal that requested assistance. It was typically sent by an individual or group that encountered a problem they could not handle on their own. The purpose of the signal was to summon those who could help.
When Turlough and the Fifth Doctor went to Sarn, Turlough sent a distress call to Trion requesting assistance for the people, who were threatened by a volcanic eruption during the Time of Fire. (TV: Planet of Fire)
When they learned of the imminent arrival of a blue star to their solar system, the Antarians sent out a distress call, but were shortly afterwards wiped out by the Valerons, who also destroyed their world, with Dynil the only survivor. (PROSE: A Universe Called Fred)
Hundreds of Time Lords, who were stranded in the bubble universe by House, used hypercubes to send distress calls. The Corsair's hypercube arrived in the main universe and found the Doctor's TARDIS. After the Eleventh Doctor arrived in the bubble universe, he heard the distress calls on Nephew's translation sphere and assumed this meant there were living Time Lords. Unfortunately, all the Doctor found was a cabinet filled with hypercubes, as House had murdered every Time Lord whom it had encountered. (TV: The Doctor's Wife)
During the Battle of Demons Run, the Doctor had a squad of Dalek-upgraded Spitfires destroy the communications array of Demon's Run so Colonel Manton would not be able send a distress call to his fleet. (TV: A Good Man Goes to War)