Who surrendered to the Patriots on October 17, 1777?
British General John Burgoyne
The surrender was the culmination of the British Saratoga Campaign. Early in the war, Britain targeted the Hudson River Valley because of its strategic importance. The plan was for General Burgoyne to lead a force south from Canada, while General William Howe was supposed to send an army up from New York (the city had been taken by the British soon after the outbreak of the war).
Instead, Howe sent his troops to take Philadelphia (which he eventually was successful in doing). This left Burgoyne facing the Patriot army on his own. Meanwhile, support for the Patriots was growing, and the Patriot army was growing along with it. At the Battles of Saratoga, Burgoyne lost to the Patriot army and was forced to retreat on October 7th.
Over a week later, following continuous assaults and retreats, Burgoyne agreed to terms of surrender, and on October 17th, his remaining soldiers marched out and surrendered their weapons to the Patriots.
While it is disputed whether control of the Hudson River Valley ended up being important to the war effort, the Battle at Saratoga had huge effects on foreign policy. France had been supporting the Patriot army with ammunition, but hadn't officially joined the war. For the most part, they wanted to see evidence that the Patriot army stood a chance of victory. More importantly, after Saratoga, France was worried that Britain would attempt to negotiate a peace, which would allow Britain and it's colonies, reunited, to attack French territory.
When the news of Saratoga reached France, they agreed to an alliance, and officially declared war on Britain in February 1778. Spain and the Netherlands followed suit over the next two years.
The failure of Burgoyne also prompted British Parliament to send a Peace Commission. However, inspired by new foreign support, the new United States refused to accept any terms except for complete independence.