One of the ways search engines determine what Google calls “PageRank” is by the number of incoming links, with more weight given to sites with high page-ranks (NB: I will use this term as the generic word to mean how a search engine prioritises how the results are displayed).
This has resulted in so-called “link spam” where multiple sites have been created for the purpose of linking from them to try and boost the page-rank of the linked site.
Since Wikipedia is one of the most highly ranked sites on the internet, and it allows anyone to create links from there, it would be a ideal place for people to create pages and links for the sole purpose of boosting their site’s page-rank.
By enforcing “nofollow” tags, it tells the search engines that these links are worthless when it comes to considering their value to the linked site. This means the incentive to fill Wikipedia with link-spam is basically eliminated.