Explosiveness is related to power
https://en.wikipedia.org/wiki/Power_(physics)
Basically, Power = work / time
Work = Force * distance
Force = mass * acceleration
Being able to say squat 600 doesn't exhibit a lot of power, because it's a slow movement. However, a lot of work is done as it requires a lot of force. It's a reason why power lifters chuckle at most exercises people do at the gym. The squat, bench, deadlift and press get a lot more work done than 500 other exercises people do combined. Think slow twitch muscles.
Explosive movements like box jumps and the clean, jerk and snatch don't exert the same amount of work because the weights used are a lot lighter. However, they are quick (full body) movements. Fast twitch muscles are used. You can't train this as much because it's largely genetic on how many fast twitch muscles you have (and based on when you started to train).
But explosive movements require strength. They say you should be at 2x bodyweight DL and 1.5x bodyweight squat before you do explosive training. The guys in the Olympics doing Oly lifting are beasts, respective to their body weight.
Those guys are Oly lifters, not power lifters. Most power lifters don't have incredible explosiveness as its not their sport. Power lifters would destroy them in their core lifts.
<a href="https://www.youtube.com/watch?v=wZeV6W1VEoM" target="_blank">[video=youtube;wZeV6W1VEoM]https://www.youtube.com/watch?v=wZeV6W1VEoM[/video]
<a href="https://www.youtube.com/watch?v=ny2DD0T8Hlw" target="_blank">[video=youtube;ny2DD0T8Hlw]https://www.youtube.com/watch?v=ny2DD0T8Hlw[/video]