to give a strict, explicit order; to charge someone emphatically about what must or must not be done
Every New Testament use of this verb is a strong, formal command. It is not a casual "told" or "asked" but a pointed, carefully spelled-out directive. In everyday Greek of the period this was the word for official orders, legal instructions, and even written bank drafts, so when it appears someone in authority is laying down exactly what is required.
Most of its appearances are in Mark, where Jesus repeatedly gives this kind of strict order to keep silent: to the family after he raises a girl from death, to the crowd after he heals a deaf man, and to the disciples coming down from the mountain of the Transfiguration. The force is real; in one scene Mark doubles the verb and adds "again and again" to stress how emphatic the charge was. Mark keeps this word distinct from the sharper verb he uses when Jesus rebukes (ἐπιτιμάω) demons and silences them.
The same verb also covers authoritative speech that is not about silence at all. It introduces a solemn warning to beware the "leaven" of the Pharisees, a formal instruction the Jerusalem leaders insist they never issued, and in Hebrews it names the dreadful "injunction" spoken at Mount Sinai. What ties these together is not their content but their tone: a distinctly marked, binding word from someone with the standing to give it, more weighty than the ordinary verb for giving instructions (παραγγέλλω).