Understanding it
Each version lists all the others, itself included: the French page points to the English one, and the English page to the French one. This two-way link is essential.
The x-default value names the page to show when no language matches, often a country selector.
Google states it does not use the HTML lang attribute to detect language: hreflang is what links the versions together.
A concrete example
Illustrative example: a French and English site
An agency publishes its site in French and English. Without hreflang, a British searcher sometimes lands on the French version in Google.
Each page now declares its French version, its English version and an x-default page. Google shows each searcher the right language.
The common mistake
Forgetting the return link
A French page pointing to the English one, with no link back, is ignored by Google. Each version must list all the others, using the same canonical addresses.