DVI cables are most often used to connect a PC to a flat screen or projector. By using a digital DVI monitor cable, a high digital image quality and resolution is achieved, as conversions to analog signals and back again are completely avoided. This provides a sharp image, high contrast, greater depth and super beautiful colors. Read more about DVI here
DVI-D connectors are pure digital video cables that have primarily been used between a computer and a monitor. These cables have typically been replaced by Displayport and HDMI cables, and therefore there is still a selection of adapters and cables to connect older equipment with new ones.
DVI-I connectors are compatible with both analog (VGA/XGA) and digital signals (DVI-D and HDMI). However, DVI-D connectors can only be used for pure DVI-D cables, but are still compatible with HDMI. DVI-D is also compatible with DisplayPort.
Mini DVI has been replaced by Mini Displayport, which Apple primarily uses in its laptops. The Mini-DVI standard is directly compatible with DVI-D, DVI-I, and VGA at full capacity.