A quick definition of specific objection:

A specific objection is when someone disagrees with something that is happening in court and gives a reason why. This helps them to appeal if the judge doesn't agree with them. There are other types of objections too, like a general objection which only says that something is not relevant, or a speaking objection which gives too much information. In parliamentary law, a specific objection can also be used to stop a motion from being discussed if it is controversial or offensive. In patents, an objection is when an examiner finds a mistake in the application, but it doesn't mean the idea is bad.