Why is musical notation important? what benefits do musicians and others receive from being able to write down and note aspects of a musical piece?

Most importantly, musicians can share their works with others.  Other people can see their musical ideas and can try and perform them too.   Nuances such as tempo, dynamics (loud soft, sweet, "harsh", are just some examples) can be understood even if the composer is not present and there is no recording to listen to.
Financial benefits can be realized from the sale of sheet music, scoring the piece, arranging the piece for bands, orchestras, etc. Conductors can lead an entire musical ensemble through the piece. 

*insert ribbon > table drop-down menu* would allow you to insert a quick table

You keep on reviving