Learn French: Arrosez les graines toute la semaine.

This is the imperative mood, which is used for giving commands or instructions. Just like in English ("Water the seeds"), you drop the subject pronoun in French when giving a direct command.

How does toute la semaine (all week) differ from toutes les semaines?

Toute la semaine (singular) means "the entire week" or "all week long" (one continuous period). If you make it plural, toutes les semaines, the meaning changes to "every week" (a repeated action).

Why do we need la in toute la semaine? Can't I just say toute semaine?

To say "the whole" or "all of the" in French, you must include the definite article (le, la, or les) after the word tout. So toute la semaine literally translates to "all the week."

How would I add a purpose to this sentence, like "so that they grow", using this lesson's grammar?

You could say Arrosez les graines toute la semaine pour qu'elles poussent. Because the conjunction pour que (so that) expresses a specific goal or purpose, it forces the verb that follows it (pousser) into the subjunctive mood.