Here is my answer. I am a native born English speaker, and I think I am quite good at English.
1. Generally speaking, to let = means to allow.
e.g. 'I will let you have that last ice cream in the fridge because you have been good",
e.g. "I will let you go now because we have been talking on the phone too long".
e.g. "my teacher did not let me finish the exam because we ran out of time"
HOWEVER, note that in some English speaking countries (UK, Australia) you can use the word 'let' in a different way. You might see a sign saying 'rooms to let'. This means, rooms are available to rent. In that specific case, 'let' means 'to lease / or to rent'. However, that is too advanced for now.
Now, let us look at 'to leave'
Generally, "to leave" means to go away.
So. In the above example, you might be speaking to a friend. It might be very late and you want to end the conversation. You will often say: "Oh, I see it is getting late - I will let you go for now, we will speak again soon"
Your friend, in reply might say "oh yes, it IS late. we had better leave this conversation for another time"
Can you see? the person with the power to control someone will use the word "let" to show they are giving permission, or in another way, "allowing" someone to do something.
The difference is that the verb "leave" means someone is going away from something.
So. The policeman can say "I will now let you leave"
That means he is controlling someone but he is now giving that person the opportunity to go away if they want.
HOWEVER, note that in some English speaking countries (UK, Australia) you can use the word 'leave" in a different way. Soldiers and sailors are given "leave" - which means official papers that mean they can go on holiday for a limited time. But I would not worry about that, as that is advanced English.
Hope that make sense.