StarCraft 2: Heart of the Swarm beta is still ongoing, and Blizzard has posted a preview of a new leveling feature coming soon to the game-in-progress.
Blizzard's adding a progression system to the multiplayer mode, in which players will earn experience, on a race-by-race basis, as they play in matchmaking and custom games. Gaining XP for each of the various factions will unlock special portraits and decals for player profiles.
Blizzard has plans for XP bonuses as well, either for specific awards like your first win of the day, or for more general happenings like XP bonus weekends and other special events. The leveling system is being added to the beta in the next patch (and will likely be reset a few times during testing), and will eventually be available in Heart of the Swarm when it's released.