A binary image is an image made from pixels using only values of 1 and 0 (binary) and may be stored using JBIG2 compression.
A small binary image is often manually designed for Bitmapped fonts or small icons. But a large image is usually the result of a digital photo or scanned picture. This kind of image is sometimes referred to as bi-tonal. Often the image is text which may later be read by a person or converted to characters using image recognition software (OCR). Using a single bit representing black and white is the smallest possible size for an uncompressed digital image and it can be compressed to be smaller still. For this reason FAX machines use this format. While black and white is the norm for these images there is no actual requirement, the two values could be any two colors. Generally one color is termed the background, a zero, while the second color is the foreground image, a one.
The easiest compression scheme is to use RLE which is very good for long areas where the value doesn't change such as a simple line drawing with large areas of background. However there are later schemes with much better compression.
JBIG stands for Joint Bi-level Image Experts Group and is an early lossless compression standard. It is often called JBIG1 now that there is a newer standard. It was developed for image transmission such as FAX machines. It will generally offer up to 50% better compression than the FAX 4 standard. It uses an arithmetic algorithm to compress future items based on what it has already seen. The encoder is called the MQ coder. Patent concerns limit its usefulness.
JBIG2 is 2 to 4 times better at compression that JBIG. It offers both lossless and lossy compression. It takes a look at the image and divides it into sections based on the particular data present in the image. Areas that are neither halftone or text are compressed the same as JBIG using the MQ coder. (See CMYK for a discussion on halftone.)
Text is compressed by using letter recognition and then capturing the area of the letter, saving it and then reuse a pointer to the data every time the character appears. This technique is very much the same as used in DJVU. Halftone is compressed similarly by capturing repeated areas.
PDF files versions 1.4 and above may contain JBIG2-compressed data. There are open-source decoders for JBIG2 including Java based which is available in xpdf. There is even an open-source encoder available.
E Ink technology can take advantage of the increased speed of a screen display using a single bit per pixel. This is call A2 mode or 1-bit mode and can be fast enough to provide motion images.