If something happens irregularly, it's uneven or unpredictable. When a worker never knows what day (or week) she'll get a paycheck, she might understandably complain about being paid irregularly.
If your elderly cat seems to be breathing irregularly, taking in uneven gasps of air, you should probably take him to the vet. And if you keep forgetting to eat breakfast, sometimes have lunch at 11:00, and other days wait to devour an enormous meal at 4:00, you are eating irregularly. Irregular things are erratic or random, and the Latin root is irregularis, "not having rules."