Broken link: A broken link is, simply, a hyperlink that doesn't work. Broken links don't lead to the location to which they were intended.
When building functioning links is such a crucial component to any SEO campaign, no website can afford to have broken links. When users come across links that don't work and 404 errors on your site, they're much more likely to leave your site for one with working links. If you have an active SEO campaign for your website, you likely put a lot of time and effort into bringing people to your website -- don't turn them away with a simple mistake.
As soon as you find broken links on your website, it's imperative you get rid of them immediately. In addition to disrupting user experience, broken links can cause significant long-term damage to any website's rankings in Google's search engine results if left unfixed. Search engine "spiders" that visit websites to determine their ranking can detect broken links. A website that's fraught with dead ends and broken links will obviously rank lower than a website whose links are functioning as they should.
Best of all, finding broken links on a website doesn't have to be difficult -- there are a number of broken link checkers online where you can check for broken links at no cost.