Should a certificate be installed when a browser offers to install it? I was accessing my internet banking site, and I found my browser asking to install some certificates noted some extensions of certificate.

Do I need to install certificate to access the site safely or can I access it ignoring the suggestion of installing certificate?

Do certificates help more in secure browsing?
Yes, your bank wants to establish a secure connection to you. To make sure that the connection is secure, a set of certificates must be installed on both your client and the bank's servers. If the website that you blurred out is correct, then installing the certificates is perfectly safe.

TL;DR: press Install to access your bank securely.