Anchor text is the text in the body of your webpage that has links (hyperlinks) from it. An example of some anchor text is: We provide keyword research to our customers. In this example the anchor text is "keyword research". The anchor text should give users an idea about the type of page that they will be going to. In the example I have given the hyperlink goes to the organic seo services page where our keyword research service is located.
Anchor text is important because it lets search engines know what pages are about. It is great for increasing the SEO value of your website as it helps search engine robots to scan your website for important information. But don't go overboard in the amount of anchor text that you have on your website. Remember, the users of your webpages are going to be viewing the page so if the whole page is full of link it will look confusing for them.