Learn Italian: Il venditore continua a spiegare la sua offerta. - The salesman keeps explaining his offer.

In Italian, the verb continuare (to continue or to keep doing something) requires the preposition a before a following infinitive verb. To say the salesman keeps explaining, you must say he continua a spiegare.

Why is it la sua offerta instead of just sua offerta?

In Italian, possessive words like sua almost always need a definite article like la right in front of them. The main exception is with singular family members, but since offerta (offer) is not a family member, it must include the article.

Does sua translate to his or her here?

It translates to his in this context because the sentence is about the salesman. However, sua is feminine to match the feminine noun offerta (offer), not the masculine venditore (salesman). In Italian, the possessive matches the gender of the thing being owned, so it would still be la sua offerta even if the seller were a woman.

What is the connection between venditore and selling?

Venditore (salesman) comes directly from the verb vendere (to sell). The ending -tore is a very common suffix used to create masculine nouns for professions or people doing an action, just like the -er or -or endings in English.