It's also an emblem of the green buddha of the north, Amoghasiddhi, and represents his all-accomplishing wisdom as lord of the karma family of activity.

The raised throne upon which masters are seated when teaching is traditionally decorated on the front by a hanging square of brocade displaying the image of a crossed vajra in the centre, often with four small swastikas in the corners. This emblem represents the unshakeable ground or reality of the Buddha's enlightenment.

Long description
Most of what is known of the Indian kīla lore has come by way of Tibetan culture. Scholars such as F. A. Bischoff, Charles Hartman and Martin Boord have shown that the Tibetan literature widely asserts that the Sanskrit for their term phurba is kīlaya (with or without the long i). However, as Boord describes it, "all dictionaries and Sanskrit works agree the word to be kīla (or kīlaka). I suppose this [discrepancy] to result from an indiscriminate use by Tibetans of the dative singular kīlaya. This form would have been familiar to them in the simple salutation namo vajrakīlaya (homage to Vajrakīla) from which it could easily be assumed by those unfamiliar with the technicalities of Sanskrit that the name of the deity is Vajrakīlaya instead of Vajrakīla. It should also be noted that the term (vajra)kīlaya is frequently found in Sanskrit texts (as well as in virtually every kīlamantra) legitimately used as the denominative verb 'to spike,' 'transfix,' 'nail down,' etc.
Mayer (1996) contests Boord's assertion, pointing out that eminent Sanskritists such as Sakya Pandita employed Vajrakīlaya Further, he argues:
it is possible, on the other hand, that the name Vajrakīlaya as favoured by the Tibetans could in fact have been the form that was actually used in the original Indic sources, and that there is no need to hypothesize a correct form Vajrakīla". "Vajrakīlaya" could have come from the second person singular active, causative imperative, of the verb Kīl. Indigenous grammar (Pāṇini Dhātupāṭha I.557) gives to Kīl the meaning of bandha, i.e. "to bind", while Monier-Williams (285) gives the meanings "to bind, fasten, stake, pin". Hence the form kīlaya could mean "you cause to bind/transfix!", or "bind/transfix!". This, taken from mantras urging "bind/transfix", or "may you cause to bind/transfix", might have come to be treated as a noun; and the noun might then have become deified; hence Kīlaya might have started out as a deified imperative, in some ways comparable to the famous example of the deified vocative in the name Hevajra, and a not unheard of phenomenon in Sanskrit tantric literature. This suggestion is supported by Alexis Sanderson, a specialist in Sanskrit tantric manuscripts whom I consulted on this problem.[3]

Fabrication and components
The fabrication of kīla is quite diverse. Having pommel, handle, and blade, kīla are often segmented into suites of triunes[4] on both the horizontal and vertical axes, though there are notable exceptions. This compositional arrangement highlights the numerological importance and spiritual energy of the integers three (3) and nine (9). Kīla may be constituted and constructed of different materials and material components, such as wood, metal, clay, bone, gems, horn or crystal. Wooden kīla are favored by shamans for healing and energetic work.[citation needed]
Like the majority of traditional Tibetan metal instruments, the kīla is often made from brass and iron (terrestrial and/or meteoric iron. 'Thokcha' (Tibetan: ཐོག་ལྕགས, Wylie: thog lcags) means "sky-iron" in Tibetan and denote tektites and meteorites which are often high in iron content. Meteoric iron was highly prized throughout the Himalaya where it was included in sophisticated polymetallic alloys such as Panchaloha for ritual implements. The pommel of the kīla often bears three faces of Vajrakīla, one joyful, one peaceful, one wrathful, but may bear the umbrella of the ashtamangala or mushroom cap, ishtadevata (like Hayagriva), snow lion, or stupa, among other possibilities. The handle is often of a vajra, weaving or knotwork design. The handle generally has a triune form as is common to the pommel and blade. The blade is usually composed of three triangular facets or faces, meeting at the tip. These represent, respectively, the blade's power to transform the negative energies known as the "three poisons" or "root poisons" (Sanskrit: mula klesha) of attachment/craving/desire, delusion/ignorance/misconception, and aversion/fear/hate.