A form is the shape of someone or something. And, when something forms, it comes into being or takes shape.
Put "trans-" and "form" together, and you get "transform." To transform is to go beyond your current shape: to change into a very different shape. And when you transform something, you change it into a totally new thing.
For example, Transformers is a series of shows and movies about alien robots who can change their shapes. Here's Bumblebee transforming himself into a car.
For another example, Cinderella's fairy godmother transforms an old, dirty dress into a new, fancy one. You could also say that the dress transforms. It transforms from old and ragged to new and sparkling.