This period of time was when dinosaurs first evolved. The continents we live on today were part of one land mass that scientists call Pangaea. The climate was hot and dinosaurs flourished after the Permian, or Permian-Triassic, extinction (also known as the "Great Dying") eliminated nearly all marine and terrestrial life. This occurred at the end of the Permian period and the start of the Triassic.
At the end of the Triassic, another mass extinction occurred. This time, 80% of the Earth's species died off. Leaving the surviving dinosaurs to adapt and evolve during the Jurassic Period.
During the Jurassic Period, Pangaea split into two land masses where dinosaurs flourished. The plant-eating giants you know and love feasted on the warm planet that was lush with green plants and tall trees Stegosaurus, diplodocus, and allosaurus are just a few of the dinosaurs that lived during the Jurassic Period.
During the Cretacious Period, the land broke apart into more pieces and moved around to create different environments for dinosaurs to evolve in different ways. I bet your favorite dinosaur (non-scientific observation is that 60% of people say triceratops, 10% of the time) lived during the Cretaceous Period. During this time, sauropods grew to their largest size and many of the dinosaurs we know and love (we see the T.Rex fan club members out there) stomped the Earth.