Completing the DLC will create an additional rift in your ending while also adding tons of Easter eggs, subtle changes and references to its story when you reach the Extended Cut conclusion. The Leviathan DLC pack will cost $10 and is coming out soon. Here's a brief rundown on the plot.
Admiral Hackett has been running black ops missions across the galaxy to hunt for an elusive creature known for killing Reapers. Nobody knows where it is, though when a Citadel scientist named Bryson picks up the trail, he is promptly murdered. After that, his loyal assistant blacks out and shoots himself, completely unaware of his actions (indoctrination perhaps?) From here its Shepard's job to track down The Leviathan.
Fans of the game have been hassling BioWare to make combat more difficult and The Leviathan DLC definitely ramps up the difficulty. Tight corridors make it difficult to plan strategies, especially when Brutes are charging at you left and right. Another intense moment comes from charging a door with power cells in order to open it. The tense part is that you have to continually go back for power cells as the power slowly drains away.
From early tests The Leviathan seems to be an action-packed, intense add-on to an already intense and action-packed game. I can't see this significantly influencing the overall ending of the story, though every additional detail just adds to the already incredibly rich story. The Leviathan DLC will cost you $10 when it is released.
Source: IGN - Leviathan Add-On Will Change Mass Effect 3's Ending