Simplified Chinese is exactly as it sounds. Its characters are formed with fewer strokes and appearance is proportionally simpler than Traditional Chinese. It was created during a movement to encourage higher literacy for Mainland China’s citizens in the 50’s and 60’s. For this reason, it is generally used nowadays to communicate only to and between the people of Mainland China and Singapore.
Traditional Chinese, as one might infer, is the written language system that has been around for thousands of years. This form of writing is still historical separation from Mainland China.