Parker was a farmer by trade, but since he'd been soldier in the French and Indian War, he was placed in command despite the fact that he was quite ill with tuberculosis at the time. Parker went on to join the Continental Army in the Siege of Boston, but was too ill to be involved in the battle of Bunker Hill.
Parker died in September, 1775. The statue of the Minuteman on Lexington green is said to be a representation of him - though since there are no known pictures of Parker, the resemblance is sketchy at best. It's the thought that counts.