We would use this sentence if the person we are writing to is about to do something new or different -- like searching for a new job, seeking a promotion, etc. You don't know if he/she will succeed or fail. You want them to tell you whether they succeed or fail. So, you ask them to tell you how things "work out," meaning to tell you what happens and whether it was good or bad for them.

Hi Bing Chen, "Let me know how everything works out for you!" The phrase "works out" means the result of a task or the culmination of some endeavour. Therefore, when we ask someone "how things are working out", we are interested to know the current status of someone's work. In your sentence, the other party wants to know if whatever you are doing is proceeding smoothly. Example: The residents have resolved their differences and things are working out well. Just as a side discussion, "work(s) out" also means to be engaged in physical exercise. (Example: Josh is a fitness buff and works out thrice weekly.") Hope this helps. Cheers, Lance

It means keep him or her informed about how things go for you in the future. By the way, we could give you a better answer if you told us what you already understand and what exactly you're confused about.