Something is varied when it covers a wide range of things. If you start out eating eggs in the morning, then have a snack of sushi, then pizza for lunch, fresh fruit with your tea, and a beef stew for dinner, you have a varied diet.
The word varied comes from vary, which means "to change, alter." Think of varied as describing something that has many altered forms or has been changed often. There are many varied ideas on how to improve the economy. The artist has painted in varied styles as his interests have changed. And a varied workout routine will keep you from getting bored.