What is the purpose of a balun?

The term 'balun' is a portmanteau of the words 'BALanced to UNbalanced'. Its primary purpose is to safely and efficiently interface an unbalanced transmission line, such as a coaxial cable, with a balanced load, such as a dipole antenna. When you connect an unbalanced line directly to a balanced antenna, RF currents can flow down the outside of the coaxial shield, turning the feedline into an unintended radiator. A balun prevents this by choking off those common-mode currents and forcing equal and opposite currents into the balanced antenna halves. It does not inherently increase antenna gain, though it helps the antenna system function as designed.