Cette boîte contient du miel que le boulanger vend au marché.

Du is the French partitive article (a contraction of de + le) used before a masculine singular noun to express “some” or “any.” It indicates an unspecified quantity of honey.

• In a negative sentence, it becomes de: Je n’ai pas de miel.
• Le miel (definite article) would mean “the honey” in general or a specific batch already known.
• Un miel would be “a honey,” which sounds odd because honey is uncountable in French.

Que is the relative pronoun for the direct object of the subordinate verb. Here, miel is what is being sold, so it’s the direct object of vend.

• Que replaces miel in the subordinate clause.
• You would use qui only if the relative pronoun were the subject of that clause (e.g., le boulanger qui vend du miel).

Contenir is a transitive verb that directly takes its object. You simply say La boîte contient du miel. There’s no need for dans, because contenir already implies “to hold/contain inside.”

• If you want to express location instead, you’d use il y a
  • dans: Il y a du miel dans la boîte.

Au is the contraction of à + le. Since marché is a masculine singular noun, à le marché becomes au marché, meaning “at the market.”

• If the noun were feminine, you’d use à la.
• If it were plural, you’d use aux.

Cette is the feminine singular demonstrative adjective (“this/that”) used before feminine nouns.

• Boîte is feminine, so we choose cette.
• Ce is for masculine singular nouns (and cet if the masculine noun begins with a vowel), ces for all plurals.