Structured data is machine-readable information in a page's code. In SEO, the most common choice is the schema.org vocabulary in JSON-LD format.
What is structured data?
With a type and its properties, you describe for example a product, an article, an organization, an author or breadcrumbs. The data has to match what the visitor actually sees on the page.
Google recommends JSON-LD because it's easier to implement, but it also supports Microdata and RDFa. You can test the syntax in Google's tools and in the Schema.org validator.
What you get out of it
For supported types, a page can get a rich result, such as product information or breadcrumbs. Correct markup still doesn't guarantee a rich result.
Structured data isn't a general ranking boost. It helps a machine describe the content unambiguously, and it doesn't replace quality, accessibility or visible text.
How it relates to AI
Structured data can make entities and relationships more precise, but Google doesn't require any special schema for AI Overviews or AI Mode. Nobody can honestly claim that JSON-LD alone raises the chance of a citation.
Use supported types and keep them in line with the content. Made-up ratings, hidden FAQs or false properties break the guidelines and earn no trust.