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 link: queries.
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.
- The links use Javascript or Flash some other method that the search engines don't recognise.
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.