Half-giants are a hybrid creature from the distant past, historical interbreeding of giants and something else. In World of Warcraft, the vrykul of Northrend are the only group to have been described as such. It is unknown how they came to be for the Titans created Giants without the ability to reproduce.
New information suggests that half-giants may not be the result of interbreeding between giants and humanoids, but rather a midpoint in an evolution of giants into humanoids.
It is also possible that vrykul being described as half-giants represents early development material that was later left out of the final release, much like the reference to vrykul being referred to as "vampiric". The term half-giant does not appear in game.