The appeal to authority fallacy, also known as Argumentum Ad Verecundium, is a fallacy in which authority is substituted for an argument. Truth, by nature, is not dependent upon people, which means those of low authority can make true statements, and those of high authority can make false statements. Therefore, even experts must defend their claims, and laymen have every right to question them.
The example I most love to give is my old biology professor. One lesson, we were learning about taxonomy, and she divided the class into male and female. We had a quiz, and were tasked with classifying various animals. One of those animals was the basilisk lizard, which is a reptile. But according to my professor, it's actually an amphibian. Naturally, especially since the girls "won" that round, a lot of the boys objected, which was met with "It is not for you to question what I teach, you just have to accept it because I teach it". "I will give you a PowerPoint presentation on why you are wrong!", one of the boys shouted back at her.
And he did. He was so annoyed about this event that he came in the next lesson carrying a list of sources showing that the basilisk lizard is, in fact, a reptile. Even this, she simply placed in the bin. The worst part about this scenario is that we asked our other professors, and they correctly identified the basilisk lizard as a reptile, only to second guess themselves when it turned out we were asking because the most qualified professor among them had said it's an amphibian. These people, who were themselves qualified professors, questioned the right answer because someone more qualified than them insisted on the wrong answer.
The simple fact is, because truth is independent of individuals, no authority will ever be sufficient to prove a point. In fact, throughout history, experts have made some very critical mistakes. Take, for example, the Great Chromosome Fiasco. If you ask anyone today how many chromosomes a human has, the correct answer is 46. But in 1921, a zoologist named Theophilus Shickel Painter concluded that we have 48 (24 x 2). Based on Painter's authority, this became consensus, and for the next 30 years, all the scientific literature said human beings have 48 chromosomes, even when photographs of all 46 were published alongside the claim.
Notice, Painter's authority was legitimate. He was quite qualified to do the work and make the claim. And he did the work before making the claim. He wasn't even lying, it was simply an honest mistake. But the "official" number of chromosomes was promulgated entirely on his authority. It was ok to question him, and it remains ok to question any and all authorities to this day. In fact, it is positively dangerous not to. No human authority is omniscient, nor are they inerrant, but they are sinners. That means they are susceptible to honest error, bias, deception, manipulation, peer pressure, bribery and corruption, and sin. Therefore, no human authority will ever be 100% reliable, and there are many reasons they may make false claims. Thus, the simple fact that they make a claim will never be enough to establish those claims as truth, and it is not unreasonable to question them.
It should be noted that there are times when authority is sufficient. Personal claims, for example. If I say "I like lemon ice cream", you can trust my authority, because it is a claim I make about myself. Similarly, my friends may be able to testify to the fact that I like lemon ice cream, and they can, based on their proximity to me, be relied upon. Certainly more so than a stranger who has never met me.
Ultimately, while appeal to authority is one of the most common fallacies, it is also one of the most lazy, as it gives the appearance of having "won" a debate with exactly zero effort. When appealing to someone else's authority, you don't even have to think for yourself, you just follow someone else's beliefs with no critical thought. Even when appealing to your own authority, you may have already put in the thought (or may not), but you're not proving your point, you're simply demanding the aforementioned laziness.
There is only one authority figure who can be relied upon 100% of the time, that of course being the omniscient God. But even God is a reasonable being, providing sufficient evidence for us to trust Him. During Jesus' ministry, He didn't run around demanding, as He very well could have, that He be believed. When people earnestly requested evidence, He gave it to them. When people insincerely criticised Him, He still said "If I do not do the works of My Father, do not believe Me; but if I do, though you do not believe Me, believe the works, that you may know and believe that the Father is in Me, and I in Him.”" (John 10:37-38). If Christ Himself, to whom all authority in Heaven and Earth belongs, still offers proof of His claims, who are we to do otherwise?