@colleenms,
I had to sign something similar when I was laid off last year. The term in my severance package did not affect my unemployment and I am pretty sure yours won't either. The company is almost certainly asking you to promise not to sue them for wrongful termination in exchange for the severance pay.
That being said get legal advice. There is usually some free legal assistance available. I was laid off as part of a large group that was provided outplacement which gave us a chance to pool questions and provide support. If your company does this, you should definitely take advantage of this.
These agreements are also negotiable. The company wants you to go away, sometimes you can get more help with outplacement or even more severance pay if you ask.
You should get legal advice from someplace other than the Internet before you sign. It should be available for free or cheap.
Best of luck.