A certificate is used to encrpyt an connection between your computer, or in this case your iphone, and a website.
Companies pay a certificate company for a certificate, as they preform some basic verification to ensure the company is who they say they are.
The certificate ensures that you are in fact talking with who you think you are online and that the connection is encrypted. So, for instance, when you do online banking, your browser connects to their certificate.
Generally, if you are getting a certificate error for a major website, you want to be very careful, because it can mean that your system has been compromised. It may be something simple, but until you figure it out, I would recommend NOT doing any banking or entering any personal information into your phone.
Sorry I could not give you more help, as I am not super familiar with the iPhone!!