Can someone explain about 'no-follow' links

I've copy and pasted the following exert from wikipedia below, but I'm still trying to get perspective on it.
1) can i have an overall perspective? and...
2) if my webpage is already indexed by a search engine, am i correct in thinking that 'no follow' links are then indeed beneficial for my site SEO and Ranking??

(from wikipedia)
While all engines that use the nofollow value exclude links that use it from their ranking calculation, the details about the exact interpretation of it vary from search engine to search engine.[8][9]
Google states that their engine takes "nofollow" literally and does not "follow" the link at all. However, experiments conducted by SEOs show conflicting results. These studies reveal that Google does follow the link, but does not index the linked-to page, unless it was in Google's index already for other reasons (such as other, non-nofollow links that point to the page).[9][10]
Yahoo! "follows it", but excludes it from their ranking calculation.
Bing respects "nofollow" as regards not counting the link in their ranking, but it is not proven whether or not Bing follows the link.
Ask.com also respects the attribute.[11]
rel="nofollow" Action Google Yahoo! Bing Ask.com
Uses the link for ranking No No No ?
Follows the link Yes Yes Yes No
Indexes the "linked to" page; No Yes No No
Shows the existence of the link;
Only for a previously indexed page Yes Yes Yes
In results pages for anchor text;
Only for a previously indexed page Yes Only for a previously indexed page Yes