Learn French: Ils ont vendu leur bateau la semaine dernière.

It is the past participle of the regular -re verb vendre (to sell). To form the past participle of regular -re verbs, you drop the -re ending and add -u.

Can we just say Ils vendu instead of Ils ont vendu?

No, because the past tense being used here (the passé composé) requires two pieces to work: a helping verb and a past participle. You must use the conjugated form of avoir (ont) followed by the past participle (vendu). Translating word-for-word, it literally means 'They have sold'.

Since 'they' refers to multiple people, why is it leur bateau and not leurs bateau?

In French, possessive words like leur (their) agree with the object being owned, not the people who own it. Because they are selling a single boat (un bateau), you use the singular form leur. If they were selling multiple boats, it would be leurs bateaux.

Why does the adjective dernière come after semaine?

While English says 'last week', French usually places adjectives after the noun. For time words like semaine (week) or année (year), placing dernier or dernière after the noun specifically means the week or year that just passed.