Why was the Battle of Bunker Hill fought?

British General Howe had captured Boston. At the time, the back bay was exactly that - a bay. Breed's hill and Bunker's hill (named after the owners of the farms where the hills were) were great vantage points to watch Boston below and across the bay. The rebels 'dug in' and created fortifications - in one night. It was a huge undertaking under the cover of darkness. From the hills, the rebel cannons could reach to some areas of Boston. Howe sent his men across the bay on boats to stop the American cannons. He sent several waves of troops marching up directly into rebel fire until the shear numbers of British troops - combined with a minimal amount of American ammunition - over-whelmed the rebels and they were forced to retreat. The British eventually held the hill but had taken a huge number of casualties from what was supposed to be a motley crew of farmers that would run at the mere sight of the royal army. If you are really interested, there is a great book called The Glorious Cause by JEFFREY SHAARA that tells about the early years of the American revolution.
English decided they would try and take Breed Hill from colonist to induce fear. It took them three tries to finally win, and they only won because the colonists ran out of ammunition.