The British were occupying Boston, ready to begin constructing fortresses on Breed's Hill and Bunker Hill to better control the harbor. The colonial forces learned of this plot and situated themselves on these two hills, ready to fight the redcoats.
On June 17, 1775, the 6000 British troops in Boston were surrounded by 15000 colonial soldiers. The British were worried that their enemies would get cannons and blast the town, so they attacked first.
The British marched up Breed's and Bunker hills to kill the colonists at the top. They suffered heavy losses due to colonist fire, but managed to get to the top of the hill. Colonist forces were ordered not to fire at the British until they got very close, to save ammunition.
However, the colonists managed to beat back the British twice, but their situation was becoming critical. One of their leaders, Joseph Warren, was killed in the retreat, along with many other colonial soldiers.
This was a Pyrrhic victory for the British, as they lost over one thousand soldiers to the colonists. This battle was the first major one in the Revolutionary War, it showed the Colonists that the British weren't as tough as they thought.