Technically the word "Kuji-in" refers only to the hand postures (mudra) and their related incantations (mantra). The related practice of making nine cuts--five horizontal and four vertical, alternating--in the air with the finger or on paper with a brush is known as "kuji kiri," nine syllable cuts. In Japanese folk-magic and Onmyodo, the nine cuts are often made over writing or a picture, to gain control of the object named or pictured. Thus, a sailor wishing to be protected from drowning might write them over the kanji for "sea" or "water".
The Kuji-in practice symbolizes that all the forces of the universe are united against evil; because of this, it was often used by the common people for luck when traveling, especially in the mountains.
Note that the syllables are shortened forms, and there are also longer, Sanskrit mantra that go with the same mudra.
The hand postures are as follows:
Jumon is On baishiraman taya sowaka. Mudra is dokko, "seal of the thunderbolt."
臨 (Rin): Hands together, fingers interlocked. The index (sometimes middle) fingers are raised and pressed together.
Jumon is On isha naya in tara ya sowaka. Mudra is daikongo, "seal of the great thunderbolt."
兵 (Pyō): Hands together, pinkies and ring fingers interlocked (often on the inside). Index finger and thumb raised and pressed together, middle fingers cross over index fingers and their tips curl back to touch the thumbs' tips, the middle-fingers' nails touching.
Jumon is On jite rashi itara jiba ratanō sowaka. Mudra is "seal of the outer lion."
闘 (Tō): Hands together, index fingers cross each other to touch opposite ring fingers, middle fingers crossed over them. Ring and pinky fingers are straight. Tips of ring fingers pressed together, tips of pinkies pressed together, but both sets of ring and pinky fingers are separated to form a V shape or bird beak.
Jumon is On haya baishiraman taya sowaka. Mudra is "seal of the inner lion."
者 (Sha): Hands together, ring fingers cross each other to touch opposite index fingers, middle fingers crossed over them. Index finger, pinky and thumb straight, like American Sign Language "I love you".
Jumon is On nōmaku sanmanda basaradan kan. Mudra is "seal of the outer bonds."
皆 (Kai): Hands together, fingers interlocked.
Jumon is On aga naya in maya sowaka. Mudra is "seal of the inner bonds."
陣 (Jin): Hands together, fingers interlocked, with the fingertips inside.
Jumon is On hirota ki shanoga jiba tai sowaka. Mudra is "seal of the wisdom fist," also known as "seal of the interpenetration of the two realms."
列 (Retsu): Left hand in an upward-pointing fist, index finger raised. Right hand grips index finger, and thumb is pressed onto left index's nail.
Jumon is On chirichi iba rotaya sowaka. Mudra is "seal of the ring of the sun."
在 (Zai): Hands spread out in front, with thumb and index finger touching.
Jumon is On a ra ba sha nō sowaka. Mudra is "seal of the hidden form," also simply called the "meditation mudra."
前 (Zen): Hands form a circle, thumbs on top and fingers on the bottom, right hand overlapping left up to the knuckles.
Each word is translated to the following meaning for Shinto.
Each word is translated to the following meaning in Buddhism.
There as many as 81 variations to the Kuji-in in certain sects of Buddhism in Japan, to say nothing of other mudra that are also used.
The kuji-in are a tool to be used in meditation, and are frequently over-simplified in popular culture as being a form of magic. This misrepresentation, along with the misuse of the mudra and mantra, has been further popularized by Dead or Alive, Tekken, and certain neo-ninja.