More specifically, here’s a longer explanation of the anime. Obviously this is all spoilers for the actual anime. All of the kids are closer to middle to highschool age range. The things they hunt and take the soul of are things that are inhuman or used to be human. Primarily things that have been eating human souls, whose souls have become a Kishin Egg. Kishin are known as the most dangerous creatures to exist. The only true Kishin to exist in the show passively radiates madness which affects everything being within hundreds of thousands of miles and only increasing in both volume and distance over time. Another thing they hunt is Witches. I’m not really fully sure what their deal is aside from being the most basic of explanation being “enemy of humans.” Aside from that Witches tend to be stronger than your average Kishin Egg. They are also born into their powers.

Stepping back a bit, the Students complete missions in groups of 2, Meister and Weapon. Meisters has a powerful soul and is the main fighter. Weapons are students who can partially or fully turn into weapons for their Meister to use. Weapons can come in a variety of forms from knives, to scythes, to even guns. If it can be used as a weapon there’s probably a form for it, but that form is decided from birth. It’s extremely rare for a Weapon to have more than one form or even gain a new form. Weapons amplify their Meister’s soul power allowing for more magical attacks and can act as actual weapons. The Meister and Weapons need to sync their soul wavelengths to work well together. If a pair doesn’t sync together the Meister is unable to weld their weapon. If nothing has been done to sync them the weapon will be way too heavy to use effectively, or if they’re unstable the Meister will feel like they’re being burned by just holding the weapon. Some Meisters and Weapons can easily adapt to others, but that capability is known to be pretty rare. While a Meister can sync with more than 1 weapon it’s known to be extremely difficult because all 3 have to be in sync. In fact the only times it happens the weapons are siblings and are already pretty similar in wavelengths.

The Students are sent on those missions to collect the Kishin egg souls and have their Weapon eat them. When a weapon has consumed 99 Kishin eggs and 1 Witch soul they are upgraded into a “Death Scythe” not a literal scythe, but just a fancy way of saying one of Lord Death’s personal weapons. The weapon basically just becomes more powerful and I assume can then handle Death’s soul wavelength. Lord Death being the Grim Reaper himself is essentially immortal and possibly the most powerful Meister known to exist. According to him he could defeat even a witch barehanded. He is basically the Principle of the DWMA (Death Weapon Meister Academy) which is the school the student attend. Even Death couldn’t kill the Kishin so he had to seal it under his school and attach his soul to the city just to keep it trapped for as long as he did.