The term callback method means the same as in normal conversations.
If I meet someone and want them to contact me, I will give them my phone number. This is known as my callback number.
Similarly, when a container starts up a filter says to the container that it is a filter and that it can be contacted by calling the doFilter method. Since every filter has a doFilter method [required by the interface] doFilter is called a callback method.
You could say that doGet is a callback method for servlets.