Learn German: Wir geben Waisenhäusern und deren Kindern finanzielle Hilfe. - We give orphanages and their children financial help.

deren and derer are both genitive plural demonstrative pronouns, but they are used differently. We use deren when it refers back to something mentioned earlier in the sentence (here, the Waisenhäusern). derer is used when pointing forward to something coming later, usually followed by a relative clause (for example, "the help of those who...").

Could I just say ihren instead of deren?

Yes, you could technically say und ihren Kindern. However, using the demonstrative deren makes the reference crystal clear and slightly more emphatic. It explicitly means "the children of those (orphanages)" rather than a general "their". At the B2 level, using deren instead of ihre/ihren is a great way to make your German sound more precise and native-like.

Why do Waisenhäusern and Kindern both end in an -n?

They are both in the dative plural because they are the indirect receivers of the help. In German, dative plural nouns almost always add an extra -n or -en to the end of their standard plural form, unless the plural already ends in -n or -s. So, the plural die Waisenhäuser becomes den Waisenhäusern, and die Kinder becomes den Kindern.