Chokan, let me try to answer you.
1) What is link popularity?
Link popularity is the number of web pages (or sites) that link to your website.
2) How do you get link popularity?
When other sites link to your site.
3) How do u get them to link to your site?
Submitting to directories such as DMOZ.org, skaffe.com etc. Also by emailing other sites requesting them to link to you.
4) Can u get link popularity without a Links page?
Yes. But a Links page is needed because some sites or directories will link to you only when you give them a link too. (Reciprocal linking)
5) If you do not have a Links page, can you give others a link?
Yes, you can link to them from any page of your website. A specific links page is not required for that. But for Google PR reasons, a Links page is a good idea.