The Union had a much larger population, far more resources, and almost all of the divided nation's industrial production capacity. In most cases, it's factors like those that determine the eventual victor in a war (see WWI and WWII for good examples of this).

But the weaker party doesn't need to defeat the stronger one. They just need to make the cost of the war greater than the price the stronger side is willing to pay. That's how the USA won its independence from Britain, after all. Part of what made the price too high in that case was assistance from the French (it was the French navy, not Washington's army, that sealed the victory in Yorktown, for example).

The leadership of the Confederacy was well aware of this and had diplomats all across Europe seeking help for their cause. If they had succeeded, history might have taken a very different turn.

A good book about Union efforts to keep Britain and other European powers out of the war: Our Man in Charleston, by Christopher Dickey.