What is @Action in WordPress?

This is called php annotations. Many of them are built-in via a standard called phpdoc (like @var), and they are used by the interpreter or the static tools (also by humans for a more structured comment).

There is another usecase for these annotations, and it’s to run some code – probably using reflections (which usually is last resort, since it’s slower), here is an example from a different system which I’m using: https://www.doctrine-project.org/projects/doctrine-annotations/en/1.13/custom.html

For example in old versions of TYPO3 you could use @inject this way.