To assign means to give someone a specific task, role, or responsibility. When your teacher assigns homework, she's officially designating which problems or reading you need to complete. When a coach assigns positions on a team, he's deciding who plays where.

The word carries a sense of authority and purpose. Someone in charge makes the decision about who does what. A group leader might assign different parts of a project to team members, giving each person clear responsibilities. A manager assigns shifts to employees. A director assigns roles to actors in a play.

You can also assign things to categories or groups. A librarian assigns books to different sections based on their subjects. Scientists assign newly discovered species to biological classifications. In math, you might assign values to variables when solving equations.

Notice that assign is different from just asking or suggesting. When something is assigned, there's an expectation that it will be done. The assignment (the task itself) becomes your responsibility. If your teacher says “I'm assigning chapter five for homework,” that's different from “you might want to read chapter five.” One is optional; the other is part of your job as a student.