An external link on Wikipedia can be any link you click that goes out to another website. The specific phrase "External links" refers to a section at the end of some articles containing them.
The most common type of external link is a link to an official website for the subject of the article. When there is no official site, there may be no External links section, which is fine. Some topics don't need them, and some websites are discouraged.
External links generally should not appear in the body of articles—that's what "wikilinks" are for. If you see a link with an arrow in the middle of an article, it probably shouldn't be there.
External links should be kept to a minimum, although editors are often tempted to add more. If you see an External links section with a dozen links, something has gone wrong—very possibly link spam.