It seems to be one of the fastest growing Internet companies in history.
Uber has grown so fast because it attracted a great deal of capital to fund its business model. It was able to attract capital because it skirts/ignores traditional safety and financial regulations on the one hand and takes advantage of desperate and unemployed people willing to put their capital to work for free (ie their cars) on the other. The combination of rule breaking and exploitation appeals to the libertarian and capitalist leanings of VCs.