When you transform you change from one thing or state to another. Picture a transformer that changes from a robot to a car. Simple, right?
Caterpillars transform into butterflies, a forest is transformed by a snowfall, and a city can be transformed by a new government or a changing economy. Transform means a big change in appearance or in essence. The Internet has transformed how we live our day-to-day lives, but you wouldn't say that moving a throw pillow has transformed your living room.