The canal was an inlet from the East River, and for part of its history you could canoe along it. By the late 17th century, however, the water was so clogged that was difficult - and inadvisable. Houses had been built alongside and both residents and local vendors used the canal to dispose of trash and sewage. When the British regarded New York in 1674 they made many improvements to the city, one of which was filling in the now-stinking canal and paving the street over it. You can thank me on behalf of all Brits later.
Nowadays, Broad Street is in the middle of the Financial District, and is mostly home to banks, and another sight you might recognize - the columned façade of the New York Stock Exchange.