It is best to think of them as functioning in a reservist fashion working in tandem with the Continental Army, which served as the main fighting force. In comparison, the militias mobilized only when needed. It is not that strange to have these kind of supplementary forces; these reserve-type units in the United States Armed Forces today. After the National Defense Act of 1916, we just now refer to these militias as each state's version of the National Guard.

We can start by recognizing their existence and their reservist function was specifically mandated in Article VI, paragraph 4 of the Articles of Confederation:

...every State shall always keep up a well-regulated and disciplined militia, sufficiently armed and accoutered, and shall provide and constantly have ready for use, in public stores, a due number of filed pieces and tents, and a proper quantity of arms, ammunition and camp equipage.

I stumbled upon a quick article by Edward Ayres, the historian at the Jamestown-Yorktown Foundation, and his sense is that their abilities as fighters were not adequate enough to merit their involvement in full-time fighting. Because of their status as normal citizens only to be called upon for short periods of time, they were too "untrained, unarmed, and uninterested." However, he does note that effective leadership was able to utilize them in a variety of auxiliary fashions.

While it it difficult to get a real sense of what roles these soldiers played in the revolution due to spotty documentation, Ayes ended up looking at the pension applications of a specific group of men from the Amherst County branch of the Virginia militia to get a sense of how they operated throughout the war:

Amherst militiamen played a variety of roles during the years 1775-1782, some being called up for as many as four or five tours, which usually lasted about three months each. Many Amherst men served as guards at the barracks near Charlottesville where the British soldiers taken prisoner at Saratoga were being held. Others were called out to fight Indians on the frontier or to relieve state forces at nearby garrisons. Some tours involved nothing more glamorous than gathering provisions or driving herds of cattle.

He mentions later that a few specific companies got called to fight in the Carolinas. One the ran away in the middle of the Battle of Camden; the other arrived too late to take part in fighting.

Once we arrive to 1786 and my specialty, Shays' Rebellion, we realize exactly why these militia men were not considered the best fighting force. The Governor of Massachusetts called upon the state militia to put down a growing insurrection in the western counties of the state, and the militia members just flatly refused. Some Bostonian merchants gathered enough funds to eventually cobble together a mercenary militia that marched west and stopped the insurrection in early 1787.

They have since been overhauled, so their feebleness in the 1700's does not speak to much about the current National Guard Units. But if I was in the Continental Army at the time, I'm not sure I would want these guys by my side.

When I was doing research, I found this bibliographic reference by Captain Robert K. Wright, Jr. 116th Military History Detachment, Virginia Army National Guard for the Army Historical Services very helpful is getting more specifics on the development of the Massachusetts militia.