There are various use cases when you might want to automatically fill a ticket's or contact's field with a value you've received from your customer. For example, you have a form built with a 3rd party system that sends you the submissions via email and you are fetching these emails into LiveAgent and you want to update the LiveAgent fields with the values from the submission.
To achieve this you can create a rule under Configuration->Automation->Rules like this one:
The rule will look in the last message and will save everything between Name: and a new line to the ticket's Name field and in similar fashion it will parse out also the email and phone.
What exactly should be matched from the content and saved in the field is defined in a rule via regular expressions.