I'll explain you this through an example.
Let's take Accounts and Opportunities where "Accounts" is the parent and "Opportunities" is the child (i.e. There are multiple Opportunities per Account.)
Now the User can relate an Opportunity to an Account either through the Potential Customer field on the Opportunity, or through the Opportunities item at the navigation bar of an Account. In this case the User needs to have "Append permissions on Opportunities and Append To permissions on Accounts."
In the present continuous tense "You are Appending the Opportunity, and Appending To the Account."