Normally a card’s color is defined by the types of mana required to cast it. Devoid changes this default so that a card can cost colored mana while still being colorless.
This has a number of benefits when combined with various other cards. For example, Eldrazi Temple produces 2 mana, but it can only be used to cast colorless Eldrazi cards or activate abilities of colorless Eldrazi.
Herald of Kozilek has Devoid itself, and also makes other colorless spells cheaper.
Devoid also makes it so that from things with protection from certain colors don’t work. For example Goblin Piledriver has protection from blue. Without Devoid, Ulamog's Reclaimer wouldn’t be able to block the Piledriver.
Eldrazi by theme are colorless; but giving them colored mana in the cost makes them harder to cast, and makes it so that they don’t all fit in all the same decks. Devoid allows these cards to be colorless while still having those restrictions.
Note that it’s not only an advantage. It can hurt you as well; cards such as Honor of the Pure will not work with your Devoid creatures, even if they cost white mana to cast.
See this article about the development of the mechanic, which goes into more detail about the decisions they made.