When an alien (who happens to look just like a human) reveals his existence to the world and uses his powers to protect others, it's inevitable that people will offer their opinions about his presence. We got a fair amount of that in Batman v Superman: Dawn of Justice, and one of the folks who was originally supposed to provide his own comedic take on Superman was former Daily Show host Jon Stewart. However, his cameo was cut from the theatrical release presumably due to unfortunate timing regarding when he exited the series, but now fans can see him on the R-rated, extended cut.
As Comicbook.com noted, Stewart's brief appearance in Batman v Superman: Dawn of Justice has been restored to the "Ultimate Edition" home media release. His inclusion is part of the 30 minutes of extra content that was deleted from the original version, So why was he cut from the movie? That likely has to do with him leaving The Daily Show last August. Stewart presumably shot his cameo sometime when Batman v Superman was in principal photography from May to December of 2014, but by the time the movie hit theaters, Trevor Noah had been the show's new host for six months. Had the movie kept its original July 2015 release, then the Stewart cameo would have still felt appropriate, but in March 2016, his appearance wouldn't have made any sense.
While taking Jon Stewart out of Batman v Superman: Dawn of Justice's theatrical version makes sense in terms of not making the movie feel dated, it makes sense incorporate him back into the Ultimate Edition for completion's sake. Also, his appearance lasts for less than a minute, so it's not like he's crucial to the plot. Like other celebrity cameos, it's just a way to show that this universe, while fictional and fantastical, shares similarities with the real world. Plus, it gave Stewart another chance to play himself in a high profile movie. His previous cameos include Evan Almighty and The Adjustment Bureau.
Jon Stewart was just one of the many talking heads included in the second DCEU entry, cut of otherwise. Other well known figures included Anderson Cooper, Soledad O'Brien, Charlie Rose, Nancy Grace and Neil deGrasse Tyson. Each of them either covered news concerning Superman's feats across the world or gave their own perspective on whether he was a benevolent figure or someone who could harm humanity in an instant. Of course, including real life news figures and celebrities is nothing new in superhero movies. The Marvel Cinematic Universe has previously included famous faces like Bill O'Reilly, Jim Cramer, Christiane Amanpour, Joan Rivers, etc.
You can now watch Batman v Superman: Dawn of Justice - The Ultimate Edition on digital HD, but if you prefer Blu-ray, you'll have to wait until July 19 for that to hit shelves.