SSL/TLS is incredibly important. Without it, your customers' data is viewable by third parties, in many cases quite trivially so. The Internet is a shared pipe; you should look at the data flowing through it as written on the backs of postcards, not safely encoded in sealed envelopes. If you want the latter, you need encryption.
But SSL would be important even without the need to encrypt your customers' data. Without SSL, users and their browsers have no way to validate the identity of websites they visit and ensure that website X really is website X and that a message from X truly came from X without modification. This allows adversaries to not only view the contents of communication but impersonate one side of the connection—again, often times quite easily. I firmly believe every nontrivial website on the Internet should utilize SSL. Thankfully the IETF seems to agree with me and is moving standards in a similar direction. HTTP 2.0 is likely to require SSL.
There are business reasons to fix your SSL, too. Even unsophisticated users are trained to look for the SSL padlock icon before divulging private data.
(As to your issue, it sounds as if your certificate is self-signed, installed incorrectly, or has missing intermediate certificates. The fix is likely simple for a professional.)
