Mission Weapons are weapons that you use only for the duration of a mission
After the mission is over, the weapon will be gone from your inventory.
Your backpack has a special slot for mission weapons and it does not take away from your normal backpack slots.
An example of a mission weapon is the Bandity Blasster which you get from Doc Mercy in the mission Medical Mystery. You use this weapon in the next mission, Medical Mystery: X-Com-municate after which it will disappear from your backpack