Extras!
In the story, Lucas is walking around in an abandoned zoo when suddenly, a huge statue of Porky, the main villain of Mother 3, appears and begins trying to hurt Lucas. Lucas runs, however his leg gets caught in a snag and he falls to the ground. When all is hopeless, Ness appears, saving Lucas using PK Thunder and PK Flash, destroying the statue. Then Wario, one of the villains featured in Subspace Emissary, arrives possessing a Dark Cannon (a weapon that's been turning the Smash Bros. characters into trophies), wanting to shoot Ness and turn him into a statue. He fails intially but succeeds once he decides to aim for Lucas, and Ness bravely pushes Lucas away to save him from the blast. He then turns into a trophy.
Lucas's depiction in Brawl has been heavily criticized throughout the years with some believing his depiction is very cowardly, which contradicts his important development throughout his journey in Mother 3. I personally don't mind it, but I understand why it isn't favorite by many. Subspace Emissary also marked the start of a now very popular ship called Nesscas, the romantic pairing of Ness and Lucas. The ship is also very devicive in terms of online opinions, but I think it's really cute and fun!
Smash Brothers features two playable characters from the Mother series, Ness from Mother 2 (introduced in the very first Smash Bros. game,) and Lucas from Mother 3, introduced in Brawl. The two heavily feature within the games' adventure mode, The Subspace Emissary. I won't explain the events of the whole story, because they are all uploaded as a movie onto Youtube which you can find here!