Engraving goes all the way back to the dawn of man over 500,000 years ago when cavemen would create murals of the different animals they had seen or hunted. This mural dates back about 30,000 years.
During the middle ages it was common for the wealthy to have their family's coat of arms engraved on something important to them such as weapons or armor. The working class and the poor would generally not have the money for a professional engraving. They would use what they had on hand such as a knife to etch their initials on belongings to prove ownership and prevent theft.
And on the pedestal these words appear:
"My name is Ozymandias, king of kings: Look on my works, ye Mighty, and despair!"
Nothing beside remains. Round the decay Of that colossal wreck, boundless and bare The lone and level sands stretch far away.
— Percy Shelley, "Ozymandias"
Engraving is our attempt to add permanence to the finite. One could argue that in the grand scheme of things all of our trinkets and treasures, all of our markings and symbols will eventually be eroded by the passage of time. However each and every attempt at extending a piece of our life out past death shapes the future by providing an insight into the past.
Perhaps the most famous example is the Rosetta Stone. For the last 1300 years no one could understand Egyptian hieroglyphs. Without this engraving they likely would have remained a mystery.
Link to different types of engravings.