Anchor text is the visible, clickable words that make up a hyperlink. In the sentence "read our guide to furnace repair," the underlined phrase is the anchor text and it points to the linked page.
Anchor text does two jobs at once. For readers, it sets expectations — good anchor text tells you where you are about to go. For Google, it provides context clues about the topic of the destination page. A link with the anchor "emergency plumber in Portland" signals to Google that the linked page is about exactly that.
