Persona 5 uses a variety of social stats that allow you to interact with different systems in the world as well as increase your relationships with others. Proficiency is one of the weirder social stats, because it mostly helps you decrease the amount of time spent on crafting. Upgrading your proficiency will allow you to make more infiltration tools as well as increasing your relationship with certain confidants.
By far the easiest way to increase your proficiency is to make infiltration tools in your room. Morgana will teach your how to do this fairly early on in the game, and the act of creating them will passively increase proficiency. It is always good to have a lock pick or two on you when venturing into Mementos or a palace, so keeping up with tool-making is important.
Another way to up proficiency is going to the batting cages or working at the Beef Bowl Shop. Both of these activities take time, but they offer rewards.
Keep in mind that investing in proficiency early is worthwhile. The higher the stat, the more tools you can make in one night.
You can also read books to increase social stats. You can check out books from the school library, or you can buy them at the bookstore. On the description for each book, it will let you know which stat will be increased by finishing it. You can read books in the school library or occasionally on the train.