It means to learn something, usually with the implication of doing it unconciously, quickly, or without effort. "What did Davi do while he was travelling?" "Oh, lots of things! But he picked up Spanish very quickly."

When someone says they are picking up the language, the course, the sport, etc... it means that they are going to take part in it. They will begin learning it and spending time to become familiar and good at it. "What are you doing these days?" "I picked up learning English." "What are you reading?" "I'm reading an English textbook." "Why?" "I'm reading it because I'm picking up the language." It's an expression to communicate that you're taking on a task. You're going to be learning it or spending time getting involved with it.

To learn the language naturally, by way of exposure, rather than deliberate, systematic effort.