It is very hard to know what event you are asking about here without having more context. There are many events in history that are known to various people as "Bloody Sunday."
The one that sticks out most in my mind, that I think of right off, is the Bloody Sunday massacre that happened in Northern Ireland in 1972.,
Northern Ireland was a place of great violence because there were two factions, one which wanted to remain part of Great Britain, and one which wanted to be part of the Republic of Ireland. The tensions were made worse by religion -- the faction that wanted to remain part of Britain was Protestant while the other was Catholic.
Bloody Sunday was a day in 1972 when a group of Catholic, non-violent protestors was attacked by soldiers from the British Army. 26 of the protestors died.
Another Bloody Sunday was the start of the 1905 Revolution in Russia. At the start of the 20th century the condition of Russian industrial workers was horrible. They had to work six days a week and put in over 10 hours every day. There was no concern shown by the owners of the factories towards the health and safety of people who worked for them and workers were not given a chance to ask for their rights with a ban on Trade Unions and any other form of association by them.
A Russian priest who took up the cause of the workers decided to present a petition signed by over 150,000 workers to the Czar on the 22nd January, 1905. When the peaceful procession reached the Czar’s palace they were attacked by the police, killing around a 100 and injuring over 300. The incident resulted in the start of the 1905 Revolution.