Laurussia formed when 3 continents Baltica, North America, and Avalonia collided with each other during the Silurian. Baltica and North America collided with each other first. Then Avalonia collided with Baltica before colliding with North America. Avalonia completely closed the Iapetus Ocean and opened the Rheic Ocean behind it.
Laurussia became part of Pangaea in the Permian. In the Jurassic, when Pangaea rifted into two supercontinents, Gondwana and Laurasia, Laurussia became part of Laurasia. The Atlantic ocean opened up in the middle of Laurussia, causing it to split into North America and Europe.