Something spontaneous happens when you're least expecting it. Spontaneous things are natural or instinctive, and they happen without warning.
If you plan to go to a movie and then you go, that's not a spontaneous thing. Ditching the movie at the last minute to go to the park? That's spontaneous. Spontaneous things happen all of a sudden, on the spur of the moment, without being planned. Spontaneous can also refer to things that happen without outside influence. Your parents will be happy if you do your chores spontaneously instead of waiting till they nag you.