1. The meaning comes from the band Rammstein's "making of sonne" behind the scenes video. While the band is watching over the video, they find a particular section humorous, leading to Richard Kruspe's (lead guitarist) overly obnoxious laugh, thus called the Sonne laugh.
2. A way to express yourself or someone laughing in an obnoxious way.
"Dude that was so funny it made me Sonne laugh!"
"I Sonne laughed so hard, milk shot through my nose!"