Learn Russian: Это твой подарок.

твой is a possessive word meaning "your", showing that the gift belongs to you. тебе is the Dative case, meaning "to you" or "for you". If you wanted to say "This is a gift for you", you could say Это подарок тебе. But to say "This is your gift", you must use твой.

Why does the sentence use the neuter word Это, if подарок is a masculine noun?

When это acts as the subject meaning "This is...", it always stays in the default neuter form, no matter the gender of the noun that follows it. It would only change to the masculine этот if you were saying "this gift" instead of "this is a gift" (for example: Этот подарок твой means "This gift is yours").

Why is it твой and not твоя or твоё?

Possessive words like "your" have to match the gender of the noun they describe. подарок (gift) ends in a consonant (к), making it a masculine noun. Therefore, we use the masculine form твой. If it were a feminine noun like книга (book), you would use твоя.

Where is the verb "is" in this sentence?

In Russian, the present tense of the verb "to be" is skipped. You simply place the subject and the description side by side. Literally, the sentence translates to "This your gift."