In more detail
The most common form is <meta name="robots" content="noindex"> in the page head. For files such as PDFs, the same instruction can be sent as an HTTP header: X-Robots-Tag: noindex. Google's guide to blocking indexing with noindex and its robots meta tag reference explain both, along with related directives such as nofollow, nosnippet and max-snippet.
An important detail: search engines have to crawl a page to see its noindex. If the page is also blocked in robots.txt, Google can't read the directive. The URL may then still appear in results, usually without a description, if other pages link to it. To remove a page from results, allow crawling and use noindex.
Sensible uses for noindex include internal search results, thank-you pages, filtered or sorted listing pages with little unique value, staging sites and thin tag archives. A common and costly mistake is launching a new site with the staging noindex still in place.
Noindex is different from a canonical tag. Canonical says "this page is a version of that one"; noindex says "leave this page out". Using both on the same page sends mixed signals.
Why it matters when hiring an agency
An accidental noindex can wipe a site's search traffic. A good agency checks for it in the first audit and after every major release. Search Console's Page indexing report lists pages "Excluded by 'noindex' tag".
Ask agencies which pages they'd noindex, and why. Our Google Index Checker shows whether any page carries a noindex in its HTML or headers.