Hreflang x-default names the page a search engine should serve to a reader whose language and region match none of your versions. It is the fallback, and the usual candidates are a language selector page or the original site. It is optional, it is easy to get slightly wrong, and it matters most on sites whose audience is wider than the languages they publish in.
What x-default is actually for
Not the default language. The fallback for unmatched readers. If your site is in English, German and Spanish, a reader in Japan matches none of them, and x-default says which page they get. Google's documentation suggests it particularly for language and country selectors and for auto-redirecting home pages, which are exactly the pages that otherwise confuse a crawler.
Which page should carry it
Either a genuine selector page that offers the versions, or the original language version if you do not have one. A selector is honest and slightly slower for the reader; the original is faster and quietly assumes English is a reasonable default, which for many audiences it is. Pick one deliberately and use the same choice across the site.
Where it goes wrong
Two failures. The x-default is added to some pages and not others, so the set is inconsistent across templates. Or it points at a home page that redirects by IP, which sends the crawler somewhere different from the reader and makes the annotation meaningless. If you auto-redirect by location, x-default should point at the page that does not redirect.
Do you need one at all
If your locales cover your audience, no: the sets work without it. If you sell internationally in three languages to readers in thirty countries, yes, because most of your visitors match nothing and the fallback is the only thing telling a search engine what to do with them.
Questions people ask about hreflang x default
Is x-default the same as the default language?
No. It is the fallback for readers who match none of your language versions, which is a different question from which language your site started in.
Should x-default appear on every page?
If you use it, use it consistently across a set. An inconsistent set is worse than none, because the sets disagree with each other.
Can x-default point at a redirecting home page?
It can, and it usually should not. Point it at the page that does not redirect, or the crawler and the reader see different things.