It is stronger than "I don't like." "I can't stand it " means "I cannot accept it."
I don't like cooked broccoli, but I will eat it because I know it is healthy.
I can't stand raw broccoli, and I will not eat it.
I can't stand raw broccoli. I don't care what dressing you put on it, I won't eat it.
I can't stand raw broccoli. I don't care what you mix it with, I won't eat it.
I can't stand raw broccoli. You couldn't pay me to eat it. I wouldn't eat it if you wrapped it in a $100 bill.
I can't stand raw broccoli. If I were trapped on a desert island with nothing to eat but raw broccoli, I would starve to death.
Joke: What's the difference between a psychotic and a neurotic? A psychotic says "Two and two are five." A neurotic says "Two and two are four and I CAN'T STAND IT."