There is something to be said about the things that can be created when limitations are imposed. There is a great documentary film called The Five Obstructions where two filmmakers, Lars von Trier and Jørgen Leth, place insane limitations on the technical process in order to force creativity. The results are incredibly interesting.

In terms of social media and apps, it's not about the creative process as much as it is about getting users to actually use these services and solve a "problem". Twitter was a response to blogs - 99% of blogs were long winded, rambling, pieces of shit that no one read or had time to read. By limiting the character count it forced people to be concise but also allowed users to easily read, digest, and find interesting stuff. Of course it had some unintended side effects like pictures of dinner, etc. Twitter before it was purely about promoting your brand, publication, or self was pretty cool.

Medium is too a response to blogs. It forces their users to use the provided styling so that everything looks good (this is subjective) and at least consistent. It also gives spectators a single place to read blogs rather than having to go to 80 different sites.

Snapchat is a bit different. I think it's a response to the issues with sexting and "once something is on the internet, it is there forever."

Twitter wouldn't have been anything without limiting the number of characters because it wouldn't have solved the problem with rambling blogs. Same with Snapchat's approach.