Anchor text is the visible, clickable part of a link. It is also where a lot of people fumble, linking the words click here as if the reader has no eyes and the search engine has no preferences.
The short version
Anchor text is the visible, clickable text in a hyperlink. It gives both readers and search engines context about what the linked page is about.
Common types
Exact match, the linked text is the target keyword
Partial match, it includes the keyword plus other words
Branded, it uses a brand name
Generic, vague text like read more or click here
The rule
Use descriptive anchor text that tells people where the link goes. Keep it natural and varied. Forcing the same exact match keyword into every link looks manipulative and helps no one.
FAQ
Is exact match anchor text bad?
Not in moderation. Used naturally it is fine. Overusing it across many links is what looks unnatural to search engines.