I appreciate your question and consider it a very valid one.
I have myself dreaded production apps when starting to apply for programming jobs, scared that they would be too complex for me to understand. But it's just a myth. Understanding bigger and complex applications just requires you to grind longer. Web appplications are IMHO, very simple applications.
I have now 5 years of working as a web developer, on both server and client side code.
Production apps are longer, and most of the time they have weird bad code. Obviously, if it's a good company, luckily the code will be cleaner, but that doesn't happen often.
Also, in a real world application, you have to account for different stuff. Like, for example, not storing users passwords in plain text, but hashing them. You'd be surprised of the amount of serious sites have no encryption of passwords, you can google that.
So it's more about the amount of things like this you have to account for, rather them being so complex you can't grasp. In general, even a production server for a site, is long, not complex, that's my opinion.
So, when starting to work as a dev, it's best to work on an already done project. You just gotta grind, and work, and ask questions.