An excerpt in WordPress is a term used for article summary with a link to the whole entry. An excerpt can be auto generated by a WordPress theme or by using the <!--more-->
tag inside the post content. Another way to create excerpts for a WordPress post is by entering the summary of an article in Excerpt field on Post Edit screen. This field is not displayed in the post edit screen by default. To enable it a user needs to click on Screen Options button on the top right corner of post edit screen and then enable it.
Excerpts allow users to display more content in less space. It is particularly useful for content rich websites such as news or magazine sites where the website owners would want to showcase more content on the front page with links to full articles. Examples of places that generally use these are RSS feeds, archived pages, and search pages. They can also be automated depending on the way they are used. Automated excerpts generally take part of the post with the specified limit of the number of words within that post. The default limit is 55 words, but this can be changed. Generally, if one has not been manually supplied for a post, one is automatically generated with the default word limit of 55 words.
In summary, there are three types of excerpts: Manual Excerpt which is entered into the post separately, Automated Excerpt which is generated from post content, and <!--more-->
tag excerpt which uses the content up to the specified part where the tag is inserted.