Questions & Answers about Мне не удалось понять это правило с первого раза.
Because this sentence uses an impersonal construction:
кому-то удалось + infinitive = someone managed to do something
In this pattern, the person is marked with the dative:
- мне удалось = I managed
- ему удалось = he managed
- нам удалось = we managed
So мне does not mean to me word-for-word in normal English style; it marks the person for whom the success happened.
Удалось is the past tense of удаться, a verb meaning something like:
- to succeed
- to work out
- to turn out successfully
- in this construction, to manage
So:
- Мне удалось понять = I managed to understand
- Мне не удалось понять = I didn't manage to understand / I failed to understand
A very literal sense is something like “It did not succeed for me to understand…”, which explains why the sentence is built differently from English.