There are several different sketches in which Bert & Ernie go to the movies, but this is the only one in which we get to see the movie they are watching.
Sonia Manzano, who plays Maria on the show and the Little Tramp here, wrote quite a few of these sketches inspired by Charlie Chaplin movies. This is how I first learned about Charlie Chaplin, except for a long time I was confused and thought that Chaplin was the name of the tramp character.
I think it's funny that the other movie patrons shush Bert & Ernie even though it's a silent movie...and then, moments later, everyone is yelling at the screen.
And now, one of the greatest Monsterpiece Theater pieces ever, "Chariots of Fur":
Based on the upload date, it looks like they added this video specifically so they could include it in a tribute to the late Jerry Nelson. Awww.
Oh, and to anyone who may be offended by Alistair Cookie holding a pipe, I refer you to René Magritte on the subject.
Now an esoteric reference in a Sesame Street News Flash:
At about 1:41 in the above video, Kermit says, "Hang in there, timepiece fans..." Jim Henson made a short film called "Time Piece" that was nominated for an Oscar in 1966.