This word consists of kanji with hiragana attached. Because the hiragana ends with an う sound, you know this word is a verb.

The kanji 点 means point, but this verb actually means to be lit or to be ignited. Think of it this way, when a flashlight turns on, it points a beam, of light.

You already learned 点ける, which is for when you turn something on. 点く, on the other hand, is an intransitive verb. That means it happens by itself. Like, "Oh look! The lights came on! That's cool (く)!"