The Siege of Boston was important both politically/in terms of morale and in strategic terms.
Politically, the siege (and the fact that the colonists won the siege) was important because it showed that success was possible. The Battle of Bunker Hill and the colonists’ general success against a real army was a sign that victory might be possible. In addition, it was important to oust the British from the place that was most closely connected to the rebellion in the public mind.
Strategically, the victory was important because it kept a major port open to the Americans. This was important given the fact that the British were generally dominant at sea. The port could serve an important economic and military role.