The phrase suggests that the loss or expenditure is so minor that it's as if only a small piece of skin has been taken from one's nose, implying that it's hardly felt or even noticed.
For instance, if a friend says, "Hey, can I borrow a cup of sugar? It won't be skin off your nose," they are implying that the request is so trivial that it shouldn't be any trouble for you to lend them some sugar.
Similarly, if someone says, "Don't worry about the cost of admission; it'll just be a few bucks, skin off your nose," they are trying to downplay the financial aspect, suggesting it's a small and insignificant amount.
The expression "skin off your nose" is commonly employed to make a request or suggestion appear more casual, friendly, or inconsequential. It's often used to minimize the inconvenience or burden of something, especially in financial or social contexts.