The ivy league colleges include: Cornell, Harvard, Princeton, Yale, Dartmouth, Columbia, UPenn, and Brown.
They are hard to get into because there are a ton of applicants for relatively few spaces. They are prestigious because if you can get into one of the "elite eight," it is like a verification that you are one of the brightest students in the United States (generally, ivy league students represent the top 1% of all students in the US).
hope this helps.