How do we get latest value of a key from blockchain?

Ethereum uses merkle tree to store data of multiple blocks. This property is used for re-organizing block

However, the number of block stored depends on sync mode. Archive nodes store the state of all historical blocks while full nodes stores only state of 128 blocks.

In addition to the existing answer, mappings are persistent, so when you're mapping a value to a key it works in the same way as when you're updating the content of state variables, state modifying functions effect storage in the same way for the two scenarios.

You mean

contract Keys{
    mapping (string => uint256) dict;


    function get(string key) public view  returns(uint256){
        return dict[key];
    }

    function set(string key, uint256 val) public{
        dict[key] = val;
    }
}

You can get the current value of any key anytime with get("a") and set new values with a new transaction on set("a",newvalue);