Date: April 19, 1775 - March 17, 1776
The Siege of Boston began right after the Battles of Lexington and Concord. The Colonial militia who had gathered to stop the British raids followed the British army to Boston... and camped outside, bottling British troops and their Loyalist allies in the city. At the time, Boston was a peninsula, attached to the mainland by a thin strip of land known as Boston Neck. With this blocked, land access to the city was cut off.
The siege lasted for most of a year, with only one major battle - Bunker Hill. But - as with most sieges - it took a toll on the city of Boston. There were shortages, particularly of firewood, and many buildings were torn down to be used as fuel. Of course, the British targeted any rebel-associated buildings for destruction. As a result, things like the Liberty Tree and the pews from the Old South Meeting House ended up inside a fireplace.
The siege ended shortly after the rebels attacked and fortified Dorchester Heights to the south of Boston - giving them the ability to fire on the harbour. Boston's governor decided to evacuate, rather than fight. On March 17, Loyalist ships sailed out of the city.
March 17 is now known as "Evacuation Day" and is a holiday in some parts of Massachusetts. The fact that it is also St. Patricks Day is... mere coincidence. (Though it is said that in ancient Gaelic, "Evacuation" means "Drinking as many pints as possible and being sick in a bin", so you never know.)