I think Criada nailed most of it, but I have a few things to add.
Try this angle: Jesus is God. Ever since creation, he had been sitting in Heaven, enthroned in glory, receiving the due worship of his creations. He is the King of Glory, perfectly good and holy.
Now, his subjects become real jerks. Because Jesus/God is completely holy, any deviation from him must be toward evil, so justice demands that the jerk subjects be dealt with. This is treason, so death or banishment would be the proper punishments. However, this is not what happened.
Instead, said Good King gets up off throne, takes form of Jerk Subjects, and comes to Earth in a glorious Virgin Birth to...Joe and Jane Nobody in the Middle of Nowhere. Besides that, he has to sleep in a feeding trough and I'm dead sure he didn't get out of there without some dumb animal drooling on him.
The Good King spends his entire life(30 + years) dealing with lowly human problems, suffering hunger, thirst, heat, cold and really bad sleeping conditions. Not to mention he lives in the backwater territory of the Roman Empire(not the nicest bunch of guys) and surely saw and felt his own fair share of injustices.
Finally, at around age 30, he begins to reveal the truth to his backward subjects, and what's his thanks? They nail him to a block of wood. To which he willingly goes.
The Cross is the greatest sacrifice of all time, not only for the pain involved there, but because of the fact that God came down to fix our mess when he didn't have to. In doing so, he endured everything we have to go through and more. He stepped down from all the pomp and glory he rightfully deserves for the sole purpose of rescuing a bunch of ungrateful wretches that didn't deserve it and really deserved to get pummeled in the worst way.
That's the sacrifice. It's the sacrifice that only the greatest Father would make for his children. It was a sacrifice of love.