What does 'Apply yourself' really mean? [closed]

"Apply yourself" means to put in the effort required to master a subject or attain some other goal. Here's a good example of the usage from A Cab Called Reliable: A Novel by Patti Kim:

From her leather-upholstered, swiveling recliner, she leaned down at me and said, "If you want to succeed here and in your life, you must focus, concentrate, and apply yourself.

It's say it's much more about exertion than about skill. I think it holds a connotation of perseverance or laboring for an extended period.

"Put your back into it" is similar.

To answer your second question, here are phrases for the scenario you gave where you work your way into a subject without seeing the whole picture.

Participation, or hands-on experience allows you to understand the practicalities, and allows you "get to grips with the problem," "get your hands dirty," or "know the business from the bottom up," or simply "get stuck in."

On the other hand, theoretical knowledge, "understanding the rationale," and "the whys and wherefores" give theoretical understanding of the situation.

Notes:
[get stuck in (the Free Dictionary) To begin doing something at once and with energy and/or enthusiasm.]
[get your hands dirty. (informal).Idioms by The Free Dictionary to involve yourself in all parts of a job, including the parts that are unpleasant, or involve hard, practical work Unlike other bosses,]