They wanted to break the legs of Jesus and the others crucified because the Sabbath was soon approaching and they couldn't have taken down the bodies off the crosses on the Sabbath because that counts as "work" and the Jews were very, very strict about not doing anything resembling work on the Sabbath. (In the Old Testament a man was stoned to death for simply gathering sticks on the Sabbath.)

They wanted Jesus and the others to die faster so they could take them down before the Sabbath. Breaking the legs will cause a crucified person to die from asphyxiation, because the legs are what allows the crucified person to push themselves up to take a breath. Without their legs they suffocate.

But Jesus had already died, which is why they didn't break His legs, and a Roman Centurion simply pierced his side with a lance to check if He was dead. But not one of His bones had been broken during His Passion, Crucifixion, or after, to fulfill a prophecy which you can find in the Bible that goes: "not one of his bones shall be broken." Psalm 34:20 is one of the verses, and it varies depending on translation, but you get idea.