The Battle of Brandywine was fought on September 11, 1777. The main combatants were the Continental Army under the command of General Washington, The British Army under the Command of Gen. Sir William Howe (with Lord Charles Corwallis commanding the main regiment), and the mercenary army from Hesse-Kassel under command of Reichsfreiherr Gen. Wilhelm von Innhausen und Knyphausen (under the Gen. Howe's Command).
The British had sailed from New York and landed at Head of Elk, Maryland with the plan to march north to take Philadelphia and to meet up with the army of Gen. John Burgoyne and as a combined force fight and defeat the rebels in a major pitched battle, thus hoping to end the war. Gen. Washington had received word of their march toward Philadelphia and gambled (using similar logic) that if he could stop them it could shorten or end the war outright.
The only major natural barrier on the road from Baltimore to Philadelphia is the Brandywine Creek that was crossed by Philadelphia-Baltimore Pike by a ford (and ferry) controlled by John Chad and hence known as "Chad's Ford". Washington resolved to set his army along the northern banks of the Brandywine, taking advantage of the thick forest and hilly terrain in the hopes of stopping Howe's advance.
Though Washington was aware of the fact that there were fords further up the Brandywine, he made the critical error of underestimating the distance to the closest usable one for the British forces and thus underestimated the time it would take Howe to set up any flanking maneuver.
On the morning of September 11, the major forces of the American and British armies faced each other across the Brandywine Creek (or so Washington thought). Gen. Washington ordered his troops to cross creek and attack the British lines (primarily those of Knyphausen) head-on. Gen. Howe had send a good portion of his army north to ford the Brandywine and hopefully flank Washington's position. Around this time Washington had been receiving reports of British movement northward on the other bank of the river, but was skeptical. As a result, Howe's flanking troops were able to get across and attack.
Luckily word had finally gotten through to Washington and he was able to turn back his advance and turn to meet the flanking element in time to save his army. Given his being out-maneuvered, victory was at this point beyond his reach. He made a hasty but strategic retreat towards Chester while Polish Gen. Casimir Pulaski make a valiant cavalry charge to distract the British, with the main bulk of his army still intact. Likely due (at least in part) to Pulaski's charge Howe decided that it would be too risky to give chase and broke off the engagement.
Though this battle ended in defeat for the continental army, it was pivotal nonetheless. This was the first time that the main American Army met the main British forces in a pitched traditional battle as opposed to surprise attacks and skirmishes. Yes, Washington had defeated the Hessians at Trenton, and Cornwallis' troops at Princeton, but these were minor elements of the British force that Washington's men outnumbered 5:1 in both cases.
There was a strong prediction that in spite of those victories, the moment Washington's men met an equally equipped (and viewed as superiorly trained) Main British force he would be crushed, and the revolution with him. Brandywine was this first meeting--and Washington lost, but was definitely not crushed. Furthermore, the loss was mainly due to miscalculations and bad gambles on Washington's part, and not due to any heretofore-presumed inferiority of his men. They were able to regroup to fight again. This ability of Washington's forces to stand up to the British and come out of the other side went a LONG way toward bolstering the morale of his men and raised many eyebrows in Europe. This combined with Burgoyne's defeat and surrender not too many day's later in upstate New York at Saratoga (thus ending Howe's plans for a combined force) directly led to the French Crown's decision to enter the war. (The wounding of the Marquis de Lafayette at Branywine probably helped as well--my editorial here).