Sectumsempra, invented by the wizard Severus Snape (under his nickname "the Half-Blood Prince") is a spell that, when uttered, acts as an invisible sword, slashing the target as a sword would.
This spell is greatly effective on living targets (humans, animals, plants), but not so effective on non-living or dead ones (Inferi, rocks, walls, etc.).
Harry Potter, in his sixth year, discovered the spell in the Half-Blood Prince's Potions book. As the summary written in the Prince's book for this spell was "For Enemies", Harry decided to use the curse on Draco Malfoy, which earned him a whole series of detentions from Professor Snape. He also tried out the spell on a whole army of Inferi, but to no avail, as Inferi could neither feel the gashes inflicted upon them nor lose any blood from the cuts.
Sectumsempra derives from the Latin "sectum" (was cut) and possibly "semper" (always).