Ok, your questions is a little inaccurate. After the battles of Lexington and Concord, the British were basically chased back to Boston. They were, and always were, in control of Boston before the battles and until shortly after the battles.
They were not able to "hold" Boston after the Continental Army had placed cannons on Dorchester Heights. Knox had gone to Fort Ticondergoga and brought back the cannons that drove the British army out of the city. The Continental army controlled the city from that point on.
Wow... well... I have no idea. Boston was held by the British until March of 1776, almost one year after Lexington and Concord.
At the start of the war, the British held Boston. The Battle of Bunker Hill was fought so they could have nearby Charlestown also.
Then the Continental Army besieged Boston. After the Continentals got cannon after defeating the British at Fort Ticonderoga, they brought the cannon down and put them on hills around Boston. This made it so the British had to leave.
But as far as right after Concord and Lexington, the British had Boston.
Do you think you could check a bit on the accuracy of this question (like did you misread it in your book or your question sheet or whatever)? The thing is that my understanding of things is that the British did hold Boston at the time of the battles of Concord and Lexington. The soldiers marched out from Boston and returned to Boston. In the words of one of my textbooks on the subject, there was so much rebellion in the countryside that "Governor Gage's authority was limited to Boston, where it rested primarily on the bayonets of his 4,000 troops."
One other quote, this one from enotes... "In the early summer of 1775, the British controlled Boston."
So... please clarify.
I agree with the previous answers, but if you are looking for the strategic significance of Lexington and Concord, they were important because of their gunpowder and ammunition supplies. The British tried to destroy these supplies because gunpowder especially was very hard to come by for colonial troops. The British supplied it in the past, and without it the troops could not fight.
Concord residents hid the gunpowder and weapons from the British troops. The British troops were successful in dumping some supplies into the river, but many of those supplies were able to be salvaged after the troops left.
Therefore the strategic failure to destroy rebel supplies in Lexington and Concord contributed to the colonists' ability to fight.
THAT WAS THE QUESTION IT WASNT NOTHING ELSE ADDED IT WAS THE FACT AFTER THE BATTLES OF CONCORD AND LEXINGTON