The narwhal, Monodon monoceros, has long fascinated sea explorers, scientists and aristocracy. This arctic whale is characterized by a single spiraled tusk extending six to nine feet, emerging from the upper jaw and through the lips of adult males. Males have the characteristic left front tooth extending approximately 8 feet and variable depending on the whale and the age. The right tooth remains embedded in the skull and measures roughly one foot. Some females may exhibit a tusk, and in rare instances a male with two tusks has been observed."

Source : narwhal.org

The function of the tusks has not been fully explained. Theories suggest that they might be:

• Sensory organs: They are known to be replete with sensory nerve fibres, and may be able to sense temperature, salt concentration, electric fields etc.
• Fighting weapons: This has only rarely been observed.
• Communication devices: Either by visual signalling, or because of their tactile sensing capabilities - through tusk rubbing.
• Ice-breaking devices: There are anecdotal reports that the (air-breathing) animals might use the tusks to break through sea ice coverings from below in order to create breathing holes in the ice.

More info. at Wikipedia