Driving for Uber seems like an interesting choice to make some extra money, and my wife and I have talked about it a couple of times. As with most things in life, it's a little more complicated than the ads make it sound. While that's not to say it may work well for you, you should check out this article on How-To Geek that does nice job of bringing up several points you may not have considered.
When you’re an employee at a company, they’ll pay around half of your FICA taxes while you pay the other half (on top of your income tax that you’ll need to pay, which is likely withheld). However, if you’re an independent contractor, you have to pay every penny of your FICA taxes. You’ll receive a 1099 when tax season approaches, instead of a W-2.