New Jersey is not a borough of New York City - it's a state. However, its north-eastern regions bordering the city essentially constitute New York's most conveniently located suburbs - only a quick PATH (or boat) ride separates Jersey City or Hoboken from Manhattan.
Over the past years, the Jersey City / Hoboken area has seen robust growth in terms of commercial and residential real estate. A substantial percentage of people living in those areas work in New York City, mainly in Manhattan. As a result, most New Yorkers now consider the J.C. - Hoboken - Weehawken - Fort Lee corridor to be the unofficial "sixth borough" of the city.