Grammar JLPT Level N5 - Lesson 7

来(く)る is one of only two verbs in Japanese that do not follow the standard rules of conjugation for Godan and Ichidan verbs. The other primary verb being する. 来(く)る means 'to come', or 'to be coming'.

• お前(まえ)もパーティーに来(く)る？
  Will you come to the party too?
• サヤの家(いえ)に来(き)ている。
  I have come to Saya's house. (I'm at Saya's house now)

来(く)る will always have the particle に or へ attached to the location that someone 'will come', or 'has come'.
The reason that 来(く)る is called a か-column irregular conjugation verb in Japanese is because the る in 来(く)る does not conjugate, but is dropped. This leaves the く being the part that conjugates. Because of this, 来る has qualities of both る-Verbs (the る being dropped), and う-Verbs (the remaining く changing depending on the conjugation). Here are some examples of how 来(く)る changes.
（き）た, （く）る, （こ）ない
来(く)る will often be seen as 来(き)ている when someone has come to a place and remains there. This is due to ている meaning 'to exist in the state of an action', rather than being exactly the same as '(A)~ing' in English. Because of this, 来(き)ている can mean either 'to be somewhere that one has come', or 'to be coming'.

• 今(いま)、駅(えき)に来(き)ている。
  I have come to the station. (I am at the station now)
• カナは駅(えき)に来(き)ている？
  Is Kana coming to the station? (Is Kana on her way to the station now?)

Sometimes the difference between these two will not be clear unless there is further context.