An objection is a way of saying "No!" to something. People offer objections to things they oppose.
An objection is a statement of protest. During weddings, you often hear the question "Does anyone object to this union?" If someone did, that would be an objection: they think the wedding is a bad idea. In court, a lawyer says "Objection!" if they think the other lawyer said something unfair or wrong. A little kid who says "I don't want eggs!" is making an objection. Any kind of disapproval is an objection. When there are no objections, people agree.