Meat stands for: M - monitoring, E - evaluating, A - assessing/addressing, T - treatment.
So when you're shoving meat up people's asses, then you're monitoring them, evaluating them, assessing them, and treating them.
Listen up, buttercup. This joke is all about taking the letters in the word "meat" and making them stand for medical terms like "monitoring" and "assessing." Then it says shoving meat into someone's butt is just like doing medical stuff. Get it? You probably don't since you are, you know, you.