[The right lion-dog in the Sudo Shrine in northwestern Kyoto (with the mouth open) - Photo © Ad Blankestijn]
"Komainu" they are called in Japanese, literally "Korean dogs," a pointer to their origin on the Asian mainland. As they entered Japan via Korea in the Heian-period, their name "Koma" is derived from the designation for the Korean kingdom of Koguryo, although the actual origin may be sought as faraway as Egypt or Iran.
The function of these mythical beasts is to repel evil. In the style of Buddhist temple guardians one lion-dog usually has its mouth open (agyo) and the other has it closed (ungyo) - for the rest, they look the same. Koma-inu are usually made from stone, although examples of bronze and ceramics also exist; wooden komainu are always kept inside the shrine and can now mainly be found in shrine museums, retired from active duty.
According to JAANUS, in case of the earliest komainu (dating from the 9th c.) the two statues were different: one was clearly a lion (shishi), the other a dog (komainu) - this last one also sometimes sported a horn on his head. Gradually, however, their shapes fused together, except for the open and closed mouth.
[The left lion-dog in the Sudo Shrine in northwestern Kyoto (with the mouth closed) - Photo © Ad Blankestijn]
As JAANUS also informs us, in the Heian period komainu were used as weights for curtains or screens in the imperial palace. These have not been preserved as far as I know, famous examples from the shrine and temple variety include the 10th c. wooden komainu kept by Yakushiji Temple, or the numerous sets in the Itsukushima Shrine (12th-14th c.).
If you are interested in the ceramic lion-dog variety, the Aichi Prefectural Ceramics Museum in Seto owns a large and variegated collection, dating from the 14th to the early 20th centuries, and from various regions.
Lion-dogs are great fun: some look more like raccoons or badgers and their expressions are invariably humorous.