Haijin: The Japanese term for a haiku poet, as opposed to "shijin" which translates more directly to "poet".
Haigo: A haiku pen-name. Also haimyo.
Hokku: A hokku is the opening stanza of a renga. Historically, haiku derived from the fact that it became popular to prepare the opening stanza of a renga ahead of time as something that would be impressive for a renga session. Eventually, the hokku began to be written and appreciated more and more independently of renga...
Kigo: A kigo is the season word that is used in a haiku to place the poem in a particular context. For example, "snow" would be a word that denotes winter and "pumpkin" would be one that denotes autumn. Over time, Japanese kigo became highly conventionalized so that there are thousands (or more) season words whose connection to the particular season is relatively arbitrary rather than strictly meaningful.
kire-ji: A kire-ji is a cutting word that indicates a transition or "thought-pause" in a haiku. Cutting words are apparently very common in Japanese haiku. In English haiku, some conjunctions may have a similar effect, but more common is the use of punctuation to indicate a transitionary point in a haiku, e.g. the use of dashes, ellipses, colons, periods, and exclamation marks: -- ... : . !
uta-makura: "Poetic pillow". A location which is traditionally famous because poems are written about it.
Haiku moment: A moment of transcendence after reading a haiku and the imagery has its sensorial impact on you. Probably the idea of a haiku moment was meant to be parallel to the brief moment of enlightenment after reflecting on a Zen koan. A haiku moment is a sudden sense of urgent immediacy as, upon completing the reading of a haiku, you feel yourself thrust fully and tangibly into the scene described.