Learn Russian: Мы говорили о том, что этот договор не имеет значения. - We were talking about the fact that this contract has no significance.

It is the direct object of the negated verb не имеет (does not have). In Russian, when a transitive verb is negated with не, its direct object often takes the genitive case instead of the accusative. This 'genitive of negation' is especially strict and common with abstract nouns like значение (significance or meaning).

Why do we need о том before что? Can we just say говорили о что?

No, you cannot attach a preposition directly to the conjunction что to introduce a clause. Because the verb говорить requires the preposition о (about), you must use a placeholder pronoun то (that/it) to take the prepositional case ending (о том). It literally translates to 'about that, that...' but in English we naturally say 'about the fact that...'

Is не имеет значения a set phrase?

Yes! While it literally translates to 'does not have significance,' it is the standard, everyday Russian expression for 'it doesn't matter' or 'it makes no difference.'

Why isn't этот договор affected by the preposition о?

Because the word что acts as a boundary that starts a completely new clause. In this second half of the sentence, этот договор (this contract) is the subject performing the action of 'not having,' so it must be in the nominative case. The preposition о only changes the placeholder pronoun то.