Well, actually it is a more complicated than perhaps you think. If I say to you, "Tell me how to get to your house", I expect you to answer straight away. I expect you to say, "Take the underground to Highgate station, and a bus from there." But if I say, "Please let me know how to get to your house", I mean "Please don't explain now if that is inconvenient; please tell me later, when you are ready, when you have time". So, "let me know" is a less direct way of saying "tell me". And because it is more indirect, it is often more polite and formal as well.
Joanne's friend Judy and her boyfriend have decided to get married. They still haven't made any detailed plans, about when the wedding will be and what sort of wedding they want. Joanne is very pleased and excited when Judy tells her. Here are some of the things that Joanne says:
And as for Kevin, he has just finished writing a report at work. It is a report on new developments in the market for cat food. It doesn't sound very interesting, does it? But Kevin is very proud of his report, and he wants to impress his boss and his work colleagues. "I might be able to let you see my report," he says to one colleague, loudly so that the whole office can hear. "When you have read it, perhaps you could let me have your opinion on it." Poor Kevin. Perhaps someone should let him know that there are more important things in life than the market for cat food.