What is a Sitemap?
Sitemaps, as the name implies, are just a map of your site - i.e. on one single page you show the structure of your site, its sections, the links between them, etc. Sitemaps make navigating your site easier and having an updated sitemap on your site is good both for your users and for search engines.
Why use a Sitemap?
Using sitemaps has many benefits, not only easier navigation and better visibility by search engines. Sitemaps offer the opportunity to inform search engines immediately about any changes on your site. Of course, you cannot expect that search engines will rush right away to index your changed pages but certainly the changes will be indexed faster, compared to when you don't have a sitemap.
Sitemaps are an important way of communication with search engines. While in robots.txt you tell search engines which parts of your site to exclude from indexing, in your site map you tell search engines where you'd like them to go.
How important are sitemap errors and how can affect your rankings
The first step would be to be sure your sitemap is up to date to begin with - and has all the URLs you want (and not any you don't want). The main thing is none of them should 404 and then beyond that, yes, they should return 200's. Unless you're dealing with a gigantic site which might be hard to maintain, in theory there shouldn't be errors in sitemaps if you have the correct URLs in there. Getting sitemaps right on a large site made a huge difference to the crawl rate and a huge indexation to follow.