The Anti-World is the world opposite to ours. Everything about it is negative, as our world is everything positive. For everything in the real world, there is a negative version of it in the Anti-World. The most basic example is where there is Matter in our world, there is Anti-Matter in the Anti-World.
The Anti-World posses a Negative version of everything in the real world. The most common thing utilized is Negative Chakra and Antimatter. If Antimatter and Matter are completely exposed to each other, the both of them destroy each other. People who use Anti-matter in their jutsu have a thin coating of chakra around it to prevent this from happening.
The Residents of the Anti-World are commonly labeled as Shadow Monsters but they are actually the Anti version of people in the real world. For example, you exist in the real world, and there exists an Anti-you in the Anti-World. All of the residents look like inverted versions of their real world counter parts, but in regular eyes, they look like shadowy blobs. Only a spectre can see a resident for what they really are.
A spectre serves as one who keeps the balance between the two, and is commonly worshipped by the residents of the Anti-World.