1/2 and 1/3 refer the small and big blinds posted after the dealer button - going clockwise around the table. In cash games, otherwise known as ring games, blinds primarily serve to ensure all players are subject to some minimum, ongoing cost for participating in the game. This encourages players to play hands they otherwise might not, thereby increasing the average size of the pots and, by extension, increasing the amount of rake earned by the cardroom hosting the game.
In your case the poker room is introducing a slightly more expensive game $1/$3 rather than $1/$2. The limits will usually dictate a slightly higher buy-in minimum and maximum and promote a richer pot overall.