"Let me know" means "tell me". But "let me know" is a more polite and friendly expression. It's very common to hear in an English-speaking workplace.
"Let me know if you have any questions" is a common way to politely offer to answer someone's questions about something. It's also a good way to end a business email or telephone call when you've given someone information and don't need to ask them for anything. For example:
Attached is a summary of our costs for this month. Let me know if you have any questions.