Why the name sapper?
A sapper is a soldier who digs. The job is older than gunpowder and mostly happens out of sight, which is the part that made it useful and the part that makes it a good name for a tunneling tool.
Where the word comes from
The English word comes from the French sapeur, a soldier who works with a sape, a trench or dug approach. Armies have had people who dig since siege warfare began.
What sappers did
When a fortress had walls too thick to break and gates too strong to force, sappers dug underneath. They cut passages toward the foundations, and in many sieges they packed the end of a tunnel with explosives and set it off. Sometimes the wall came down. Sometimes the defenders had already dug a counter-tunnel to meet them.
The same skill carried into the First World War. British tunnelling companies dug beneath German lines on Messines Ridge, and in June 1917 they detonated 19 mines in one morning. Engineers, who are still called sappers in the British Army, did this work for the whole war.
How it relates to sapper.sh
Your local server is behind a wall too: a home router, an office firewall, a network that does not let outside traffic in. You do not open a hole in that wall. Your machine digs out, making an SSH connection to sapper.sh and holding it open, and visitors arrive through that passage.
Nothing on your side has to be exposed to the internet first. The tunnel runs from the inside out, the same way a sapper's passage ran from the trench toward the target.