Jumping on a case means you'll remove another player's token on the murder scene and putting one of your own there, effectively making you the first player.
Although being the first player isn't always something good.
That said, for you to make your action you have to go to the crime scene (it does not involve players getting to jump around the board).
You can check the entire rule here:
Rulebook page 14 wrote:
Get a Jump on the Case (1 Time)
If a player’s detective is in the same location as the scene of the crime marker, he may pay 1 Time to get a jump on the other detectives on the case. To do so, he removes the hero marker that is currently on the scene of the crime marker and replaces it with one of his own. If his hero marker is still in place at the end of the phase, he then becomes the new first player, as described in “Changing the First Player” on page 15.
I added the underlines for emphasis on what this action actually does.