n : a written order for the payment of a sum to a named individual; obtainable and payable at a post office
Basically you take $300 to the post office, turn it into a money order, they charge a nominal fee, and you mail it to someone. That person exchanges it for $300 at a post office (or bank that accepts them). Since only the name you sent it to can cash it, it is similar to a cheque.
It's like the Templars form of 'banking' in the times of the Crusades - people paid their gold into one Templars 'Bank', and were given a written receipt. They could then cash that receipt in any Templars 'Bank' and get that amount of money out. Saved them from travelling bandit-ridden roads with coaches full of gold.