Majors and Ultras are uniquely more powerful versions of ordinary Fallen, Hive, Vex and Cabal enemies that you might battle during a Story Mission or Strike.
Majors have yellow name tags. They also have more health, own more powerful shields that recharge faster, and have better Artificial Intelligence. These enemies come in various names and types. You can I.D. them because of their yellow names.
Ultras have a skull mark on their name tags. They are even more powerful than Majors. In Additional to better stats, shields and A.I like the Majors, Ultras have circular AoE abilities that knock you back if you get too close.