Learn Russian: Я смирился с тем, что это местная особенность. - I came to terms with the fact that this is a local feature.

The verb смириться (to come to terms / to make peace) requires the preposition с + the Instrumental case (meaning "with something"). But you cannot attach a что (that) clause directly to a preposition in Russian. You have to use a placeholder pronoun, то, and put it in the required case. The Instrumental case of то is тем, giving us с тем, что (literally "with that, that" or "with the fact that").

Is there an easy way to remember the meaning of the verb смирился?

Yes! Look at the root: мир means "peace". Смириться literally means "to make peace with" or "to reconcile oneself with". The -ся ending shows that it is a reflexive verb, meaning you are reconciling yourself to the situation.

Why is the adjective местная in the feminine form?

It modifies the noun особенность (feature/peculiarity). While nouns ending in a soft sign (-ь) can be masculine or feminine, nouns ending with the suffix -сть (like особенность, радость, or новость) are almost always feminine. Therefore, the adjective must be feminine to match.

Since особенность is feminine, shouldn't это change to the feminine эта?