Learn Russian: Для меня это большая честь.

You can see it is feminine because it is paired with the feminine adjective большая (great). Nouns ending in a soft sign (-ь) can be either masculine or feminine, but честь is a feminine 3rd declension noun. This means it shares the same base case endings as the irregular feminine nouns мать and дочь that you are studying in this lesson.

Why use the neuter word это when честь is feminine?

In this sentence, это means "this is" and acts as a generic pointer introducing a new concept. When used this way, it always stays in the fixed neuter form regardless of the noun's gender. If you wanted to say "this honour" (modifying the noun directly), you would have to match the gender and use эта честь.

Why is меня used here instead of мне?

The preposition для (for) always takes the genitive case. Меня is the genitive form of я. Learners sometimes confuse this with the dative мне (to me) used in phrases like мне нужно (I need), but для never takes the dative case.

Does большая always mean "big"?

Literally, it means "big" or "large". However, when paired with abstract nouns like честь (honour), проблема (problem), or разница (difference), it translates more naturally as "great" or "significant".