After Moses begs for death because the Israelites are too heavy for him, the LORD answers:
Assemble for me seventy of the elders of Israel, men you know for true elders and authorities among the people, and bring them to the meeting tent. When they are in place beside you, I will come down and speak with you there. I will also take some of the spirit that is on you and will bestow it on them, that they may share the burden of the people with you. You will then not have to bear it by yourself.
Although the seventy were already true elders and authorities, their authority differed from Moses' in two important ways. First, theirs was a natural authority, derived no doubt from God-given wisdom but still conferred on them, not by God, but by those around them who recognized their wisdom.
Second, theirs was not an authority that imposed a burden on them. Sure, they may have worried about the people who brought their problems to them for help, but in the end, if someone didn't follow their advice, or even ask for it in the first place, it wasn't their problem.
Now, I called these two ways the elders' authority differed from Moses', but the second difference is really just one aspect of the first. God tells Moses that He will give the elders the spirit of Moses with the stated intention of them sharing the burden of the people with him. When Jesus taught that the leaders of His Church were not to lord it over the others but to serve them, He was building on the foundation of the seventy elders of Kibroth-hattaavah. (The seventy also prefigure the Sanhedrin and the College of Cardinals; the burden-bearing-to-lording-it-over ratio hasn't always been properly maintained.)
What is it about the spirit of Moses that makes it a burden-bearing spirit? Well, the seventy are made prophets; even Eldad and Medad, who hadn't made it to Moses' tent, prophesy back in the camp. So they know something of the glory of God, of the truth of He Who Is. To know God is to be impelled to communicate Him to others. More specifically, for someone in authority to know God is to be impelled to lead those under your authority into communion with Him. And the people whom God called out of Egypt were, at best, fickle in their appreciation of His glory and truth, and not particularly interested in communion with Him for its own sake.