The Previous Tappan Zee Bridge was built during the Korean War, and the design was pared down to use less material, which was in short supply. The bridge connected Rockland and Westchester Counties over the widest part of the Hudson River. The decision to place the bridge here was mostly political, and I recommend that you read some of this bridge's intersting history.
The bridge was designed to last only 50 years, and, although it did last 61 years, many engineers were worried about its possible catastrophic failure. The reduced design allowed for no redundancy if just one part failed.
It's named for the Tappan Native American Tribe with the Dutch word for "sea" tacked on.
You can also load my new Tappan Zee Bridge along with this one.