Learn German: Die Bienen sammeln Nektar, um Honig zu produzieren. - The bees collect nectar to produce honey.

The phrase um ... zu translates to "in order to" and expresses a purpose or goal. It introduces an infinitive clause separated by a comma. The word um starts the clause, and zu sits right in front of the dictionary-form verb (produzieren) at the very end of the sentence.

Why is Honig placed before the verb rather than after it?

In an um ... zu clause, the verb phrase (zu produzieren) is always kicked to the very end of the sentence. Any objects or extra details, like the noun Honig, must be placed between um and the verb.

Why are there no articles before the nouns Nektar and Honig?

Both Nektar and Honig are uncountable mass nouns being used in a general sense. Just like in English, German drops the article when talking about substances generally (the bees collect "nectar", not "the nectar").

I know the singular is die Biene, so why does it end in an -n here?

The word Bienen is the plural form of die Biene. Feminine nouns that end in -e in their singular form almost always form their plural by adding an -n. Because they are the subject doing the collecting, the phrase is in the nominative case, which uses the plural article die.