If an item is monochrome, that means it uses only one color on a differently colored background. In a monochrome monitor, these pixels have only one color phosphor. The picture is created with, say, black dots (or lines) against a white background. A monochrome image pixel can have two values, on (white) or off (black), and this can be represented by 1-bit as either 0 or 1. Most printers are monochrome, meaning they only print black toner on white paper.
If an image is One-bit that means 1-bit of information is sent to the pixel on the screen. That bit can turn the pixel on (white) or off (black). All 1-bit images are black-and-white. On amonochrome monitor, the pixels can't deal with more than just that one bit of data so that's all you can ever get is black and white.