Cimzia is one of nine biologic medications for RA. As Brad mentioned, they are the "big guns" among the treatment options and are used for people with moderate to severe RA who do not respond adequately to the DMARDs, such as methotrexate, Arava, sulfasalazine, etc. Biologics are fairly new class of drugs - the first (Enbrel) only came on the market in 1999. However, they have a huge impact on the lives of people with RA, making it more possible than ever before to go into remission.
Which biologic you choose to start with tends not to matter much, unless you have certain medical conditions that should not be mixed with some of the Biologics. For instance, people who have MS should not take a TNF blocker.
Cimzia is a TNF blocker - the medications in this class include Enbrel, Humira, Remicade and Simponi. Most of these are done by injection, although Remicade is an infusion. Often people with RA start with Enbrel and if that doesn't work well enough, move onto another biologic. Your rheumatologist may have a specific reason to recommend Cimzia over another TNF blocker, so you may want to talk to them about that in more detail.
As with any other drug, how you respond to Cimzia is very individual. I know people for whom it has worked very well and others who didn't respond to it. The only way you'll know is to start taking it. It usually takes about two months or so to fully kick in, but if it's working, you can expect to see signs of it much sooner. It usually starts with having a bit more energy and moves on from there. Primary side effects of the Biologics include being more vulnerable to infections, fatigue for a couple of days after your shot, perhaps a bit of gastrointestinal upset and upper respiratory infections. Most of the time, the side effects are very manageable.
RA pain comes from two sources: inflammation and damage. When you control the inflammation, the pain usually goes away. That is, unless you have damage to your joints. How long have you had RA? Do you have deformities, or other kinds of damage? If so, you may benefit from seeing a pain specialist - it might be something to discuss with your rheumatologist.
good luck! Please keep us posted on what happens?