A variation of the word "shrug," connected to the word "muggle" (which means commoner), denoting indifference, surrender, and acceptance of defeat to what the user perceives as an everyday occurrence. The "cutesy" nature of the word further underscores the user's indifference, as does the plural suffix.
"I failed another organic chemistry exam today. Shruggles. Good thing I decided I don't want to be a doctor anymore. I want to be a lawyer."