What will be in order that they see, know and understand?
Radak: I will do these wonders so the Goyim will put to heart and understand that I took Yisrael out of Galus.
Why does it mention seeing and knowing?
Malbim: Seeing is physical. Understanding is intellectual, via putting the matters to the heart.
Why does it say "Hashem" and "Kedosh Yisrael"?
Malbim: Hashem created the existence. Kedosh Yisrael alludes to His Hashgachah Pratis over Yisrael due to their deeds. He conducts them miraculously, above nature.
Why does it say "Bera'ah"?
Radak: This wonder is a new matter, so an expression of creation is used.
Malbim: Beri'ah is making something out of nothing; only Hashem can do so. Asiyah is fixing a matter via changing its form, e.g. making a Kli from metal, without creating the metal. If they will see only a physical Beriyah, they already knew that it was not chance; Hashem's hand did this. Rather, all will understand - Chachamim and fools - that Kedosh Yisrael did this above nature.