Why did the battles start?

The battles of Lexington and Concord began on April 19, 1775 because British regulars under General Thomas Gage marched from Boston to seize colonial weapons, gunpowder, and military stores stockpiled in Concord and to arrest Patriot leaders Samuel Adams and John Hancock, who were known to be in Lexington. The deeper reason was the collapse of normal government in Massachusetts. After the Coercive Acts of 1774 closed Boston Harbor, voided the colony's 1691 charter, and replaced its elected council with a royal one, the Massachusetts Provincial Congress assembled at Concord and Cambridge in October 1774 as an extralegal alternative government.

It organized a Committee of Safety, authorized companies of minutemen who could turn out at a moment's notice, ordered towns to gather provisions, and accumulated arms and powder around the colony. Gage was instructed in secret orders signed by Lord Dartmouth on January 27, 1775 to suppress the rebellious assemblies and use force. He chose Concord as his target because intelligence reports identified large stores there.

On the night of April 18, 1775 Gage sent about 700 grenadiers and light infantry under Lieutenant Colonel Francis Smith across the Back Bay in boats, then on a 17 mile march through Lexington to Concord. He hoped surprise would let the column complete its mission and return without bloodshed. The colonial intelligence network proved superior. Joseph Warren learned of the plan in Boston, dispatched Paul Revere and William Dawes by different routes, and the alarm reached every village in Middlesex County by lanterns and church bells before the British column reached Lexington.

Captain John Parker assembled the Lexington militia on the Green at dawn to make a public stand and warn the British column that the country was alert. At Concord, militia from surrounding towns gathered above the North Bridge. After the brief skirmishes at Lexington and Concord, the running fight back to Boston turned into a 16 mile gauntlet because thousands of militiamen from across the region streamed in to fire at the column from cover.

So the immediate cause was a military raid on a weapons cache, but the underlying cause was a year of British attempts to disarm a colony that had built its own government, and a colony that was prepared to defend itself with force.