The の in that sentence nominalizes (turns it into a noun) the phrase before it, then the で acts as it does in the other examples on that page.
今日 は 雨 だった (It rained today.)
今日 は 雨 だった の (The fact that it rained today)
今日 は 雨 だった の で (Due to the fact that it rained today)
The で in this type of sentence is actually the ~て form of the common です verb and often times the “second half” of the sentence is not needed because it has already been stated or is obvious. In these cases です is not converted to the ~て form since the sentence is not continuing. Also, in these situations, の is often contracted to ん.
A: どうして 車 で 行きました か。
B: 雨 だった の/ん です。