Larf is simply a playful way of spelling laugh. It's good to say that you "larfed" instead of laughed, because, well, laughed is plain and ordinary and is used for every day situations, while larf is the result of something more unexpected and spontaneous. This is the crux of larf's meaning. It is used mostly from unexpected and spontaneous moments.
We sat by the cozy warm glow of the evening fire, me and my other. It was so serene and pure. Suddenly, she sneezed and farted at the same time. We larfed together in cackling harmony.