The word form has several meanings:

1. A shape or structure that gives something its appearance. A sculpture takes form as the artist molds the clay. Ice crystals form beautiful patterns on winter windows. When you see storm clouds beginning to form, you're watching them take shape in the sky. In this sense, form is what makes something recognizable: a triangle has a different form than a circle, and a butterfly has a different form than a caterpillar.
2. A type or variety of something. Democracy is a form of government. Soccer is a form of sport. When your teacher asks you to write a story in short form, she means a particular type of writing with specific characteristics. Scientists talk about different forms of energy: heat, light, and motion are all forms that energy can take.
3. A document with blank spaces to fill in. When you visit a new doctor, you fill out forms with your name, address, and medical history. Permission slips and registration sheets are common forms.
4. How well someone is performing. An athlete in top form is playing their best. A musician might say she's not quite in form yet after a long break from practice. When someone asks “how's your form?” after you've been sick, they're really asking whether you're back to your normal self.
5. Verb: To bring something into existence or shape, or to come into existence or take shape. Clouds form in the sky. You can form letters with a pencil, form a club with your friends, or form an opinion about a book after you read it.