Standing up for your rights and not being taken advantage of is one definition of being assertive. It also means communicating what you really want in a clear fashion, respecting your own rights and feelings and the rights and feelings of others.
Assertion is an honest and appropriate expression of one's feelings, opinions, and needs.
It takes self-analysis, and then practice, but the results are worth it. Being aggressive means standing up for yourself in ways that violate the rights of others. Aggressive behavior is typically punishing, hostile, blaming, and demanding. It can involve threats, name-calling, and even actual physical contact. Most people are not assertive for fear of displeasing others and of not being liked.