@cineebon Hey! It might be better to think of の as “the one that…” or a nominalizer like のは that is replacing some information that can be inferred through context. @nekoyama did a great job of breaking down the differences between the inclusion and omission of の in two sentences in the post above.
Let’s take a closer look at the second sentence that appears on the grammar point’s page, 昨晩からの雨はやっと止んだよ。 - “The rain that started from yesterday evening finally stopped.” If we were to omit の, the sentence would sound something like “Rain from yesterday evening has finally stopped.” The omission and the sentence’s translation both leave something to be desired. The の is essential saying “that had been falling” or “that started (falling).” Since this information can be determined through context, the verb (降っていた) is replaced by の.
As you continue on your Japanese journey, you will find that Japanese people will go out of their way to omit information if it can be inferred through context.
Let’s take a look at the third sentence on Bunpro, おじいちゃんはポーランドでの思い出をだんだんと忘れてきた。- “Grandpa has been slowly forgetting his memories of Poland.” The の here could be replacing “time lived” or “time spent,” so “The memories (from the time spent) in Poland are what my grandfather has been forgetting” could be implied given the context.
To sum up:
昨晩からの雨 - The rain (that has been falling) since last night.
ポランドでの思い出 - The memories (from the time spent) in Poland.
彼は彼女への愛情でいっぱいのメッセージ - The messages filled with love (that) he (sends) her.
今までの対立 - The conflict (that has been ongoing) until now.
I hope this helps. Cheers!