There are many possible reasons the most likely being that the link to your site is from a newly-indexed page. If it's only been a few days and neither website is really popular then Google has not spidered the link yet.
It may take a few weeks for Googlebot to even find the link, then maybe more days or weeks for it to list it in its index for
Other possible reasons:
- Google doesn't show all links to your site, only a portion.
- The links to your site could use
rel="nofollow" and won't be counted.
Your best bet is to sign up to Google Webmaster Tools. Once your site is verified there you will get a much better picture of links to your site and other goodies. Another useful tool is Open Site Explorer but often it will be behind Google etc.