What is Charlie Chaplin's assembly line making in the eating machine scene of “Modern times”?

It's probably part of the point the film tries to make that we can't tell what's actually assembled on the assembly line.

When assembly lines became common in the early 20th century, one big point of criticism was that they were thought to alienate the workers from their work and from the product they produced. Previously, a worker had typically manufactured an individual product from start to finish (they were exceptions, but that was the basic idea). On the (then) new assembly lines, the workers only ever did one repetitive step in the process, and probably never even saw the finished product.

The idea was that, in order to experience job satisfaction, the worker would need to identify with the product they made ("I made this shoe, I made it well and I'm proud of it"). But on an assembly line, this connection was seen as broken.

So it's probably on purpose that Chaplin's character (and the audience with him) not only never sees the product he's working on to completion, he doesn't actually have a real clue what he's producing in the first place.

The scene is likely meant to be representative. There's no obvious use for what Chaplin is doing in the scene. The key is that

1. Chaplin is working on an assembly line (Henry Ford started his assembly line in 1913, so audiences would be familiar with the concept)
2. Chaplin is doing something repetitive and meaningless. Wikipedia describes the plot thus

The Tramp works on an assembly line, where he suffers greatly due to the stress and pace of the repetitive work on the assembly line. He eventually suffers a nervous breakdown and runs amok, getting stuck within a machine and throwing the factory into chaos;

As an Everyman, the audience is meant to empathize with The Tramp (Chaplin) and his plight as a "cog in the machine" in the scene. So it doesn't matter what he's building, just that he's doing it over and over, until it drives him mad.