Answer:
The British wished to capture Bunker Hill because this hill is one of the highest sectors of the Boston Peninsula, so that control of this sector would give them visibility and total defensive military capability over the city of Boston.
The Battle of Bunker Hill took place on June 17, 1775, during the siege of Boston, and was one of the first battles of the American War of Independence. The American rebel forces were led by General Israel Putnam and Colonel William Prescott. Major General William Howe was commander of the British Army. Regardless of its name, the battle was fought mostly on Breed's Hill adjacent to Bunker Hill. The British won the battle when their third attack drove the Americans to escape, but the British lost more than 1,000 soldiers. Although the British achieved their goals in battle, they could not dismantle the Boston siege.