I've only had one coffee and all these questions lol
Moses mediated between God who is Holy and sinful people. Sinful people cannot stand before God and plead their righteousness for none is righteous. God used both Moses and Jesus (God-man) to mediate between himself and his people. Through Moses the Mosaic Covenant (law etc) and through Jesus the fulfillment of the Mosaic covenant and mediating the New covenant.
For there is one God and one mediator between God and mankind, the man Christ Jesus, - 1 Timothy 2:5.
But in fact the ministry Jesus has received is as superior to theirs as the covenant of which he is mediator is superior to the old one, since the new covenant is established on better promises. - Hebrews 8:6.
You could say simply that a mediator reconciles to opposing parties. And in Christ we are reconciled to God, Jesus pleads our case.. we can see an example here -
My dear children, I write this to you so that you will not sin. But if anybody does sin, we have an advocate with the Father—Jesus Christ, the Righteous One. - 1 John 2:1.