Learn German: Wir verstehen den Gedanken, weil die Macht des Gedankens groß ist. - We understand the thought because the power of the thought is great.

It is in the genitive case (showing possession: "of the thought"). The word der Gedanke belongs to a small group of "mixed" N-declension nouns. While regular N-declension nouns just add an -n in the genitive (like des Jungen), these mixed nouns add an -ns (des Gedankens).

Wait, so why is it den Gedanken in the first half of the sentence?

In the first half, the thought is the direct object being understood, so it is in the accusative case. For mixed N-declension nouns, the accusative and dative cases just take the standard -n ending. The extra -s (-ns) is strictly for the genitive case.

Could I say die Macht von dem Gedanken instead of using the genitive?

Yes! In everyday spoken German, people frequently replace the genitive with von plus the dative case (von dem Gedanken). However, using the genitive (die Macht des Gedankens) is standard in written German and sounds a bit more formal and elegant.

Why is the verb ist pushed all the way to the end?

This is because of the word weil (because). It is a subordinating conjunction, meaning it introduces a dependent clause. In German, dependent clauses always force the conjugated verb (ist) to the very end of their clause.