"Este assunto é de grande importância."

Translation: This subject is of great importance.

[Barbeito]

I think "assunto" would be better translated as "matter".

[Lahure]

My dictionary translates assunto as subject,matter or plot. So I imagine it would really depend on the situation to which it refers. Tough stuff this indeed is without a tutor!

[TiagoMoita_PT]

Agreed, unless the context is school-related.

[Floklo]

Shouldn't "affair" also be a good translation for "assunto"?

[ZuMako8_Momo]

That could work... but not for all meanings of the word "affair."

[phaeluis]

Also accepts: "this subject is very important".