The hreflang tag (also referred to as rel="alternate" hreflang="x") tells Google which language you are using on a specific page, so the search engine can serve that result to users searching in that language.
Introduced by Google in December 2011, the hreflang tag allows you to show search engines what the relationship is between web pages in alternate languages. It's useful when you've created content that's specific to a local audience. The hreflang tag adds a signal to search engines that a user querying in language "x" will want this result instead of a page with similar content in language "y".
For example, if you create a Spanish-language version of your English-language homepage, you would tag it as "Español" by using hreflang="es" so that searchers with an IP address that a search engine has reason to believe is in a Spanish-speaking country are served that page in Spanish instead of the English version. This can decrease your bounce rate and increase your conversions by making sure your target audience lands on the version of your page most appropriate for them.
Hreflang can also be used to show that you have content targeted toward variants of a single language. If that's the case, you can target your pages even more specifically by extending the hreflang tag with annotations that indicate which region the content is localized for, e.g. Spain (hreflang="es-es") versus Mexico (hreflang="es-mx"). This is particularly useful to geotarget users to control for variations in currency, shipping, seasonality, and culture.
Hreflang is a signal, not a directive. That means that other SEO factors may override the hreflang tag and cause a different version of your page to rank higher.