Line 100: GRAPHIC1 is one of the C128 bit-map modes. BANKn does nothing until a memory-accessing command such as PEEK or POKE occurs. BANK15 is the default configuration on powerup. There are many more configurations, of varying usefulness, than the standard 0-15.
Line 110: Doodle! was a popular drawing program for the C64 and the pictures created with it were viewable on the C128.
Lines 120, 140, 160 and 180: There are no commands in Basic or the OS to change which RAM bank the Video Interface Controller displays, so these lines use the 'traditional' PEEK-POKE method to change only the two bits in the MMU Ram Configuration Register (RCR) at location 53534 that control that capabilty. Changing these bits before each picture is loaded in allowed the user to see each picture fill the screen.
Lines 130, 150, 170 and 190: The B parameter in the BLOAD command specifies which RAM bank data will be loaded into, independent of any BANK statement in effect. On an unmodified C128, B2 and B3 would 'roll over' to B0 and B1. P is the start address. The filenames are the sample pictures included on the Doodle! floppy disc.
Lines 230-310: Cycle through the 4 pictures, look for keypress to END the program and return the display back to normal text mode.
Lines 340, 350: READ DATA values to AND/OR with bits in the RCR that should not be changed.

A fairly simple Basic program that uses standard commands -- no new I/O locations, no programming 'tricks' -- to access the new RAM banks. PEEKing and POKEing the MMU RCR would be necessary even on a non-modified C128.