>What does "authority" mean in a Buddhist context?
That's a fantastic question, and the short answer is: "given my expertise is in the Theravada world... how authority works is complicated". An overly simplistic answer is: the number of years of a monk's seniority is the easy and fairly-reliable gauge of a monk's authority.
It would take a good 1-hour Dhamma Talk for me to explain what I know. Most people would be bored, and possibly even uninspired after hearing the non-tldr answer. Do you really want the non-tldr answer?
My experience is in a Tibetan tradition. In that context, "authority" derives partly from lineage, i.e. who your teacher's teacher ('s teacher, etc.) was. It comes partly from their training and experience; and it depends partly on what you are hoping to learn.
Some "senior" Tibetan monks derive their authority from their birth-family; being the nephew of a very senior monk conferred "authority" on the discredited Sogyal Rimpoche. Other monks are authoritative because they've spent decades meditating in a cave.
But really, I don't think authority is a good guide for choosing a teacher. They usually say you should try a few, and see which one works for you. But that's risky. In general, choosing a teacher is laden with risk, because you're going to commit a lot of time to that relationship. It's probably best not to start :-)
> the number of years of a monk's seniority is the easy and fairly-reliable gauge of a monk's authority
Authority, or expertise?
Authority requires either enforcement, or widespread recognition, or both. The government has authority because it has the ability to use violence. Doctors have authority because most people view them as authority figures.
Does the average Buddhist say "that monk has X years of seniority, so I'm going to take him by his word"?
That's a fantastic question, and the short answer is: "given my expertise is in the Theravada world... how authority works is complicated". An overly simplistic answer is: the number of years of a monk's seniority is the easy and fairly-reliable gauge of a monk's authority.
It would take a good 1-hour Dhamma Talk for me to explain what I know. Most people would be bored, and possibly even uninspired after hearing the non-tldr answer. Do you really want the non-tldr answer?