It means, "I've got a gun and you're going to do my bidding and/or be my hostage. " No one gets the benefit of the doubt about guns.
The school was right to arrest him.
Schools are far more controlled than the rest of society: You do not enjoy the same breadth of rights inside a school as you do outside. This is for good reasons: Schools hold trusting defenceless innocents.
You can't wear clothing with threatening or violent words or images, you can't wear insulting statements, your person or backpack is far more likely to be searched: Schools are different, and they should be. Hundreds of children are housed in closed, intimate spaces, and there is no freedom to get up and move away: The government is compelling you to be in your room, in your seat, with the other children from your town, and you have no choice.
So-
Rights are not the same, nor should they be. Responsibilities are stiffer and more specific: If a school goes no peanuts, you can't have them. Period. At halloween, masks and plastic weapons are not allowed. Lots of rights are curtailed inside a school.
So, the school was right to involve the police: An adult may have just told someone they have a gun. There are too many vulnerable people there to handle it any other way.