This is a custom unit from the Campaign. It does not exist in Standard play.
The Leviathan is an extremely powerful flying Zerg hero unit found towards the end of the single player campaign. It is not a unit that the player controls, but rather a tough opponent. It is also expected to be the location used between missions for the Heart of the Swarm expansion. 
Shatter The Sky
During the single player mission Campaign/Shatter the Sky the Leviathan will appear after the second Coolant Tower is destroyed accompanied by a brief cuscene where it is described as the largest Zerg creature on record. It will then patrol the center of the map, spawning more air units for the player to deal with until it is killed.
During the final campaign mission, Campaign/All-In if the player didn't kill the Leviathan in the Shatter The Sky mission, or opted not to do that mission at all, the Leviathan will join the fight around 70% charge on the artifact and will stay out of reach of your defenses. It will once again continue to launch additional air units for the player to deal with until killed.
The Leviathan has the ability to launch Mutalisks and Brood Lords for no energy cost without a cooldown, although the AI will spawn them over time or slightly faster in response to being attacked. The units spawn as eggs or cocoons as appropriate and will spawn in to the units after a few seconds.
Additionally the Leviathan has a direct attack which requires 125 energy in which it will launch a powerful single target attack, much like a Yamato Cannon. This attack deals 500 damage and has a 6 second cooldown.
The final ability this unit has is Bio-Stasis. This is a small area of effect attack which deals no damage but stuns all effected units, preventing them from performing any action for 10 seconds. This ability costs 125 energy and has a 20 second cooldown.