Action refers to the height of the strings above the fretboard/neck of a guitar. For fretted instruments, the action should usually be as low as possible. For unfretted instruments played with a slide, the action height is less critical and can be quite high.
The action on a stringed instrument is determined by how the nut and bridge are set up, and also to a lesser extent by whether the neck is is bowed. Usually the action will be significantly higher towards the bridge end of the neck than it is at the nut.