- to enter into somewhere like enter into a room (방에 들어가다),
- something came into my ear (귀에 뭐가 들어갔어요)
- James entered a school (제임스는 학교에 들어갔어요)
Just anything moves inside something/somewhere, so it can be like going into, comming into, entering into something/somewhere.
다니다, not 다나다, is a word we use to say going somewhere "on a regular basis as a member of the place ". So it's normally used for school, institute, company, church, etc. Not for just one time visiting. For example, 학교/학원/회사/교회에 다니다.
Hope it can help you!