This minor fast day marks the beginning of the siege of Jerusalem as outlined in 2 Kings 25:1
And it came to pass in the ninth year of his reign, in the tenth month, in the tenth day of the month, that Nebuchadnezzar king of Babylon came, he and all his army, against Jerusalem, and encamped against it; and they built forts against it round about.
As a minor fast day, fasting from dawn to dusk is required, but other laws of mourning are not observed. A Torah reading and Haftorah reading, and a special prayer in the Amidah, are added at both Shacharit and Mincha services.
(Adapted from Wikipedia)