Gilnean is the native language of the Gilneas Humans. It is technically just a dialect of the Common language and both languages are completely mutually intelligible. The Gilnean accent itself is meant to sound somewhat like the European Cockney accent to those not native to the region.
Although the Gilnean humans essentially became a separate race by transforming into Worgen, they do not speak a separate worgen language. For a short time during the Cataclysm Beta, Worgen players were able to choose to speak in Gilnean, but it has since been removed from the game. This has been met with mixed reaction from players as they are now one of the few races without a race-specific language. However, from a linguistics point of view it is unlikely that a community which has been closed off for only a couple of decades (as the Gilneans were) would develop an entirely unique language in itself, opposed to a different accent.