what is private key and how this key work ?
The way Bitcoin was designed, it is built on the blockchain which is often described as an open ledger. The public keys are on the public ledger for anyone to see how many Bitcoins are in an address, and all information about transactions including where they go and how much and what comes in and how much and where it leaves. What it doesn't tell you is who those addresses belong to and how to access them.
This is the reason for the private key. It's the only was to access an account. Anyone that has it can move Bitcoins off the address. It unlocks that address, hence the name "key".