Trenton, 26 December 1776 - Painting and Story

According to the U.S. Army Center of Military History, Washington’s troops were poorly clothed and hungry when they attacked at Trenton: 

Confident that the ill-clad and ill-fed Americans would fade away when enlistments expired at the year's end, General William Howe withdrew a major portion of his force from New Jersey to the comforts of Manhattan island. Washington realized his army's only chance of survival lay in a victory over the remaining scattered garrisons of the British and their Hessian mercenaries.

When the nearly frozen Americans attacked, however, they were victorious:

Colonel Johann Rall, the garrison commander, attempted to form a line of defense on King and Queen Streets with two regiments and the Knyphausen battery. Aware of Rall's plans, the Continentals, supported by General Henry Knox's artillery and heartened by the presence of Washington, overwhelmed the guns at a dead run.

The loss of the artillery position caused Rall's regiments to withdraw. Their powder damp, deprived of artillery support, their commander mortally wounded, the surviving Hessians surrendered.

It was a stunning, unexpected victory for the attackers.

American enlistments, for a large number of men, were set to expire.  The victory at Trenton helped Washington to keep his troops together long enough to win, again, at Princeton.

The impact of these two victories—at Trenton and at Princeton—had far-reaching consequences for America. According to the Army Center for Military History: 

These two engagements assured the survival of a small core of Continentals and, in turn, the survival of the American cause of Independence.

Or, as the British historian G.M. Trevelyan put it:

This was a long and severe ordeal and yet it may be doubted whether so small a number of men ever employed so short a space of time with greater or more lasting results upon the history of the world.

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