Altermagnets are pretty interesting because their most defining feature is not the magnetic order in the materials. They look like ordinary antiferromagnets where the spins of adjacent atoms point in opposite direction and compensate each other, so no large magnetic fields are created. What differentiate altermagnets from antiferromagnets is how the electrons with different spin behave. When pulling current through altermagnets it will consist of purely spin up electrons along one crystal axis and purely spin down along orthogonal crystal axes. Thus the spin currents have a 'alternating' pattern, giving the name altermagnet. This is primarily exciting for the field of 'spintronics' which is all about creating technologies using spin currents.

Not all altermagnets are equally interesting, many antiferromagnets can be reclassified to altermagnets but they are generally insulating. (fun fact the first ever measured and textbook antiferromaget MnF2 is actually altermagnetic) So materials discovery of new altermagnets is important to find metallic, semi-metallic or even super conducting altermagnets.