Jesus had spoken of being "lifted up" in John 3:14-15 and John 12:31-33 as the means of his death, and the result of his death--salvation for all people. The cross was inevitable. Athanasius observed that the Messiah's death had to occur by acts of others (not just a calm deathbed in old age or illness) in order to gather up and defeat, in his body, even the anger and hatred and cruelty of mankind.
The execution device used by the Romans was designed to inspire fear and horror, as condemned criminals and traitors were punished by what was often an agonizing, multi-day ordeal in an area visible to passers-by, thus encouraging order in the populace who were often conquered people resentful of Roman occupation. It was an upright stake, the base buried in the ground, and a crosspiece, carried by the condemned criminal, attached either at the top or a short distance from the top. Both Matthew and Luke mention the inscription attached above his head, so it appears that was the style used, and it is carried forward in Christian symbolism today*.
So if we look at the symbolism inherent in all these things, what might we see? Not all of these are explicit in scripture, but meditating on these ideas can be useful. And there are probably more meanings we could bring out; God is infinite in his ability to plan and create meaning for us.
- The upright stake united heaven and earth, as the Incarnation had done
- The crosspiece stretches in both directions, and Psalm 103:12 says "He has removed our sins as far from us as the east is from the west."
- The crosspiece stretched Jesus' arms out wide, as a symbol of the Father's arms being open to us; and some say, as the measure of the breadth of his love.
- The crosspiece, going in both directions, could also symbolize uniting Jew and Gentile: Galatians 3, especially verses 14 and 28.
- The wood shows he absorbed for us the curse given in Deut. 21:23, "anyone who is hung on a tree is under God's curse." See also Galatians 3:13.
Of course, these are not just "interesting meanings" -- our Savior really did die a brutal death on that torture instrument. He suffered pain, humiliation, thirst, embarrassment, fatigue and many other hurts to pay for humanity's sin and rebellion.
And he did it just for you.
* Footnote: there are some who believe this symbol is of pagan origin and so should not be used by Christians. That assertion lacks credible evidence. The cross was a symbol that offended both Jew and Gentile, but paradoxically brought hope and salvation to Christians (see Galatians, especially), and so it has remained the primary symbol of our faith.