Originally Posted by PaulMycroft
in a strict sense the "nofollow" tag does not exist.
There are two ways you can guide search engines in your pages using "nofollow".
This meta-tag instructs any internet robot (aka crawler) to not index this page (don't store any information, don't return it in the search results) AND not to follow any links to other pages.
<META NAME="ROBOTS" CONTENT="NOINDEX, NOFOLLOW">
The NOFOLLOW value here means the search engine should not use the links on this page to discover new pages to crawl. You would use that if you have links and pages that you don't want indexed and are volatile, such as random pages and or highly dynamic pages.
However, the nofollow [here] will not securely hide other pages from the SE, because any other webmaster can use the same links as you do and the search engine crawler discovers them on this path. So make sure that the page you want out of the index have a "NOINDEX" themselves.
Also, it is unclear what influence this NOFOLLOW has on weight the search engine assigns to it in the ranking algorithm. Nothing says that it should not be counted.
This NOFOLLOW value in the relationship-attribute of an anchor link is a more recent invention by Google. It indicates, that the search engines ranking algorithm should not assign any weight to it when calculating page rank of the page the anchor tag points to.
<A ... REL="NOFOLLOW">...</A>
Google invented this notation, because lots of people left hundreds of thousands of meaningless and context less links in collaborative websites such as Wiki, Blog or Forum sites. All these links where generated by programs and were a nuisance for any webmaster, blogger, wiki admin to remove. By allowing this notation, the webmaster can declare certain types of links to be w/o value to the search engine, so taking away the incentive to generate them mindlessly by program everywhere.
I hope that helps you understand
P.S.: To clarify, a "nofollow"-tag would be <nofollow ...> ... </nofollow>, which neither case above is. Strictly speaking "nofollow" is an attribute value used in two different tags/attributes.