Learn French: Quand tu récupères la calculatrice, tu me la donnes s'il te plaît ? - When you get the calculator back, you give it to me, please?

When using two object pronouns in French, 1st or 2nd person pronouns like me, te, nous, and vous always come before 3rd person direct object pronouns like le, la, and les. Since me is 1st person, it takes the first spot.

What exactly does la stand for here?

It stands for la calculatrice (the calculator). Because calculatrice is a feminine noun, you must use the feminine pronoun la to mean it in this sentence.

Why doesn't the sentence use the future tense after quand?

French usually requires the future tense after quand for future events, which would be quand tu la récupéreras. However, casual spoken French sometimes uses the present tense for immediate requests like this, treating it more like an if-then scenario.

Why is the question phrased as a statement (tu me la donnes ?) instead of using inversion?

In everyday spoken French, it is very common to ask a question by simply using standard subject-verb order and raising your pitch at the end. This makes the request feel friendlier and less rigid than the formal me la donnes-tu ?.