What do you understand by the word “suffered”?
That during His whole life on earth, but especially at the end, Christ sustained in body and soul the wrath of God against the sin of the whole human race. This He did in order that, by His suffering as the only atoning sacrifice, He might deliver us, body and soul, from eternal condemnation, and gain for us God’s grace, righteousness, and eternal life.
Why did He suffer “under Pontius Pilate” as judge?
So that He, though innocent, might be condemned by an earthly judge, and so free us from the severe judgment of God that was to fall on us.
Scripture references
Is it significant that He was “crucified” instead of dying some other way?
Yes. By this I am convinced that He shouldered the curse which lay on me, since death by crucifixion was cursed by God.