It was Preparation Day, and Jesus had already died on the cross. The Judeans knew that people should not remain on a cross on a Sabbath, so they asked Pilate to break Jesus's legs and take Him away. But Jesus was already dead, so there was no need to break one of the legs. Though one of the soldiers stabbed Jesus with a spear, resulting in blood and water coming out.
John described these things because he was witness to it "so that you may believe" (19:35). From the description, Jesus was dead-dead (since he was stabbed and hung on a cross by Romans who mastered killing people on a cross), not in a near-death experience or pseudo-death that some people talk about. But not only that, John talks about a few Scriptures that got fulfilled (where the past descriptors describe the present).
The "no bone breaks" part could reference Exodus 12:46, Numbers 9:12, or Psalm 34:20. In context, the Exodus and Numbers verses talk about how to do Passover. Passover commemorates the time when the angel of death "passes over" the Israelite community back in Exodus because of a substitution, and in a similar way, Jesus was the substitute who took on the penalty of sin. Additionally, Psalm 34 talked about David praising God with God ultimately delivering the righteous, and in a sense God likely intended on preserving Jesus's bones (since he will use them later...).
The "look on Him whom they pierced" part references Zechariah 12:10. Zechariah 12 is actually a future prophecy on piercing/striking/afflicting, and various people did look at Jesus literally pierced on the cross. Not only that, but Zechariah also wrote about a great mourning. In a sense it could happen during Final Judgment, but the mourning in response to Jesus also happened in the real world in Acts 2. God knows prideful attitudes well enough to make the prediction.