To Apply
To Submit An Application, To Propose
transitive verb, godan verb
I must say humbly that I want to get into this position, so I'm planning to apply for it and to submit an application.
申し込む isn't just about applying, though. It's about officially communicating desires, whether you want to propose marriage, challenge someone to a game of tennis, or even offer a donation to a good cause.
The readings come from the word 申す and the kanji 込, stuck together... humbly.
JLPTのテストに申し込むのを忘れてしまった。
I forgot to apply for the JLPT exam.