Black and white (monochrome), only has two "colors", black (ink or toner) and white (no ink or toner). Black and white scan mode is typically used for documents that contain text, where everything that is a printed character displays as black on the scan and the background white (unprinted). Black and whtie mode forces everything darker than a certain threshold to black and everything else as white. This makes most standard documents easier to read and a better representation of the original.
Grayscale contains shades of grey (a continuous scale from black to white) and is used for reproducing images or documents that contain more than just black printed text. With Grayscale mode, the scan will reflect more of a "photograph" of the document, showing anything that has some color (including imperfections such as wrinkles and creases).