VPESR is an acronym (a word composed of the first letters of a phrase) that stands for Valence Shell Electron Pair Repulsion.
It's a scientific theory in the field of chemisty, and it predicts the shape of a molecule based on what atoms form this molecule.
If you want to understand the meaning of the name, you can devide it into
Valence shell electron
-electrons that are on the "outside" of the atom and can form bonds with other atoms
and it's the repulsion of these electrons that is being predicted.