General Howe, had previously captured New York City and originally proposed to move north, where Burgoyne was. What caused the change of plan?
General Howe had originally proposed to London to move north to support Burgoyne (and hopefully split off the four New England states and New York from the southern colonies). He thought better of this and proposed to attack Washington at Philadelphia, because this was the "principal" American army, and attacking such an army followed the classic tenets of warfare. London gave the okay on the condition that Howe also sent a force from New York City to support Burgoyne. This he did (nominally) by sending Sir Henry Clinton north, but with insufficient force to reach Albany.
What ultimately defeated the Burgoyne Expedition was the fact that the local colonial leaders eventually raised a militia army of over 15,000 men that surrounded him at [Saratoga]. This was larger than Washington's army, which is to say that it was a totally unexpected result. More to the point, these Americans were able to fight Burgoyne from behind bushes and trees, the kind of battle in which the Continentals excelled, rather than in open field.
With the benefit of hindsight, the ultimate result was a case of "win one, lose one," not the worst result in the world. Moreover, the British never expected to "lose one," at Saratoga. If they had followed the original plan, they might have lost both Burgoyne's and Howe's armies in the wilderness and with them the war. Instead, they ended up with the American capital and the defeat of the "main" American army as contemplated by Howe. Without the offsetting American victory at Saratoga, this would have been good enough to win the war.