Learn Turkish: Onlarınki güzel bir hediye ama bizimki daha özel. - Theirs is a beautiful gift, but ours is more special.

It turns a possessive word into a pronoun, exactly like turning 'their' into 'theirs' or 'our' into 'ours' in English. By attaching -ki to the genitive forms onların (their) and bizim (our), you create onlarınki and bizimki. This lets you avoid repeating the word hediye (gift).

Why does bizimki use an -im ending before the -ki, while onlarınki uses -ın?

The pronouns ben (I) and biz (we) have irregular genitive (possessive) forms. Instead of taking the usual -in suffix, they take -im, becoming benim and bizim. The -ki suffix simply attaches to whatever the genitive form already is.

If bizimki means 'ours', why isn't it pluralized as bizimkiler?

Any plural suffix added after -ki matches the number of the object being owned, not the number of owners. Since the sentence compares single gifts, it remains singular: bizimki (our gift). If they were comparing multiple gifts, it would be bizimkiler (our gifts).

Why is the word order güzel bir hediye instead of bir güzel hediye?