I also find the paragraph confusing. At least some of it is pretty close to being nonsense in my opinion. So this is the best help I can offer: Authority= the power to give orders or make decisions. “Formal” can mean “public or official”. So I interpret “formal authority” to mean authority someone has because of their occupation. A police officer or a doctor, for instance, has an authority that is officially recognised. to serve=to hold a particular office, position, etc. : They served on the jury. She served on the city council for years. He served for five years in the army. back (someone or something) up or back up (someone or something)= to give help or support to (someone or something): I'll back you up if I think you're right. She backed her argument up with written evidence. It's time to back up your words with deeds!