Think of hot, humid, steamy weather as being so unpleasant that you feel "mugged" by it when you step outside. That's one way to remember the meaning of muggy.
"It's not the heat! It's the humidity!" That's what your grandma says when she wants to complain about muggy weather. Muggy means a combination of humidity and heat that makes you sweaty and uncomfortable and long for air-conditioning. You might be cursing the cold and the snow today, but mark my words, come August and the muggy dog days of summer, you'll be nostalgic for the cold.