I cannot understand what is the purpose of digital and analog boundary modules embedded in an IC for testing. What are their function?
They are basically switches that allow any two pins to be connected to the internal test buses AB1 and AB2 which are then brought out to the external pins AT1 and AT2 where they can be measured.
It's basically a huge internal analog multiplexer, eliminating the need to physically probe all of those pins individually in the test fixture.
As shown, the ABM probably includes the ability to disconnect each external pin from the corresponding core connection, and to probe either side of that connection.