How DNS works

A few days ago, I posted a birthday card to my mother who lives in Sri Lanka. I posted it from the local post office in Kingston upon Thames, England. Once I put it inside the post box, the delivery process started, and now it was the postal service's responsibility to deliver it to the correct person. So, when the local post office worker who picked up my letter, did they know my parents' exact house location? No, they didn't. But at the end of my address, it said the country was Sri Lanka. They then knew that if this letter goes to Sri Lanka, then the postal service there will be able to deliver it. So, the next stop of the mail was Sri Lanka. Once the card reached the main postal sorting facility in Sri Lanka, would the worker who picked up the letter know the exact address location? Maybe not, but if they don't, they could look for the city...