Learn Russian: Люди не хотят подчиняться, когда им приказывают. - People do not want to obey when they are ordered around.

It is the object of the verb приказывают (order). As you are learning in this lesson, verbs of communication (like giving commands) take the Dative case without a preposition to show who is receiving the message. Literally, it translates to "when [unspecified people] give orders to them."

Does the other verb, подчиняться (to obey), also take the Dative case?

Yes! While this particular sentence doesn't state who the people don't want to obey, подчиняться is a verb of submission that follows the exact same rule. If you wanted to add the object, you would put it in the Dative case (for example, подчиняться командиру — to obey the commander).

The English translation uses the passive voice ("are ordered"). Why does the Russian use the active verb приказывают (they order)?

To translate "they are ordered," Russian often uses an active verb in the third-person plural ("they" form) but simply drops the subject они (they). By omitting the subject, it implies that some unspecified, general group of people is doing the ordering. This is the most natural way to express this type of passive idea in Russian.

Why are both подчиняться and приказывают in the imperfective aspect?

Because this sentence describes a general truth about human nature. Imperfective verbs are used to express habitual actions, ongoing states, or general facts. If this sentence were describing one specific, completed event (like "they didn't obey when they were given the order yesterday"), perfective verbs would be used instead.