Not sure of current IRS regs but what they are doing is sub-contracting work out to you. They don't have to pay matching SS or carry workmen's comp so it saves them $$. You will simply have to file under your SS# and then on your tax return, you will calculate the correct SS, etc. It may be that you have to pay this in quarterly...as I said, rules may have changed...they are always doing that! LOL The best thing to do is if you take the job, consult an accountant for current regs. If you get a business license, it depends on the state you are in and their rules but you can also file for an IRS Tax ID#. There is so much paperwork to do!!
If you do take the job, the company will send you a Form 1099 at the end of the year rather than a W-2. This is what you will use to file taxes on your income.