This is the site of the World Trade Center, a seven building complex that was destroyed by terrorists on 9/11.
After much debate and consideration, it was decided to build another complex of five buildings, as well as a memorial park on the same 16 acre property managed by the Port Authority. Originally, the largest building was going to be called the "Freedom Tower", but for some reason the name was changed to "One World Tower" (the name of one of the the previous buildings making up the Twin Towers). The construction began in 2006.
The building, including a communications tower, will reach to 1776 feet. The height was chosen for its symbolic value to the U.S. (the year of National independence). The tower will be the tallest in the U.S., and one of the tallest in the world. It will be a commercial building, with a 50ft lobby, offices floors, tv broadcast floors, restaurants, and an observation deck.
There has been quite a bit of controversy over this site. Originally, people were divided over if there should be new buildings here, or just a memorial to the 9/11 victims. Now, there is a controversy over building one skyscraper over two, like the original WTC towers. Some people feel that the skyline should be replaced, and that it would be giving in to the terrorists to create something new like the one tower that is being built.
Construction has been slow, with deadlines being pushed back over and over. There have been various problems, including where the building would be located, safety concerns, decision making, etc. At the moment, the tower is slated to be finished in 2013.
4/7/12 Update: The One World Trade Center is now 100 stories tall.
If you would like to see the construction site, there is a viewing platform to the SW of the site, on Liberty St. Just before the platform entrance on Liberty St. is the Tribute WTC Visitor Center.
Links:
WTC.com
NYC-Tower.com
Wikipedia.com
CBSNews Story
NYTimes Article, with multiple links to other WTC articles