Compression can be translated as minimizing of digital information. There are two major types of compression: Lossy and Non-Lossy compression. Compression is most used in raster and meta images, not often in vector images.
Lossy Compression
An image processing software will remove information that it more or less redundant to the human eye. The advantage with lossy compression is that it gives a very high degree of compression. The compression is often 5–30 times. The disadvantage is that the original information will be lost. A format that uses lossy compressions is JPEG.
JPEG - The compression method used in the format with the same name.
Non-Lossy Compression
When you use a non-lossy compression algorithm all original information will be saved in the image. The disadvantage is that the compression ratio is much lower. The compression for a grey scale image is often about 50% and for a black & white image much higher.
Formats that uses on non-lossy compressions are GIF and BMP.