Until now, there were two known magnetic phases: ferromagnetic and antiferromagnetic.
The best analogy I've seen, though significantly over-simplified, is a great way to visualize the basics magnetic phases. Think of any given material as being a highway, and the electromagnetic energy within that material as two types of cars: blue cars and orange cars. It may be useful to think of the highway as a "North/South" highway, as in magnetic poles, but again, that is a significant oversimplification, and only meant as an illustration, not an explanation of what is actually happening within the material at a quantum level.

A ferromagnetic "highway" is basically a one-way road; the conditions of the road only allow blue cars to move in a single direction, no other color or direction of travel is allowed. This phase attracts only blue cars moving in one direction, and repels orange cars, as well as blue cars moving in the opposing direction. This type of "highway" is what creates what we commonly know as magnetism.

An antiferromagnetic "highway" allows both colors to travel equally in both directions; this phase of motion has an equal amount of force in both directions regardless of a car's direction or color, and so this type of "highway" is what we would find in non-magnetic materials.

The new phase of magnetism is called altermagnetism. In a conventional antiferromagnet, both kinds of cars generally experience the same road conditions. In an altermagnet, the roads effectively favor different kinds of cars depending on which direction they travel. Travel along one direction, and the blue cars might be favored. Travel along another, and the orange cars might be favored. Importantly, neither kind of car dominates the entire road.

That's the unusual feature of altermagnetism: the car's behavior depends on direction, even though the material has no net magnetization.