Jenny70. Nofollow is just a code for the search engines to not give as much credibility to a link. Your link will still show and when you click it, it will go where ever you set it up to go even if the site you post it on has made it a "nofollow" link.
The reason site owners do this is because they may be ok with people posting links on their blogs or sites, but by making a link nofollow, you're essentially telling the search engines that you don't vouch for that link.
If you can find good sites that use "dofollow" links, that's a great place to get backlinks because the search engines will view it as being endorsed by the site you posted the link on. That's basically how it works.