"Cat" is short for category, and the symbols you see are the type of move they are. There's physical, special and status moves. The orange and yellow one is physical, the blue one is special, and the grey one is status.
Physical moves deal damage based on your attack stat, and special moves deal damage based on your special attack stat. Status moves don't deal damage but often inflict statuses on the opponent or raise/lower stats.
Hope I helped!
Source: This and knowledge