Hashem told Moshe that he will harden Par'oh's heart and cause him to chase after the Jews. Hashem will then take His revenge on Par'oh and the Egyptians and they will know that I am Hashem.
Didn't they know that already? They are not chasing the Jews already just because they were so beaten by the plagues that they were aware of the God of the Jews and chose not to start up with Him again. Why does Hashem have to force them to forget that knowledge and chase after the Jews, just so He can beat them up again. Is that not like kicking the guy in the ribs on the floor after you have beaten him senseless? What was the point? The Even Haezer even says Hashem had to make them forget the plagues in order to get them to chase after the Jews! It seems so superfluous - the knowledge of God had already been achieved!
The Ramban says that Hashem wanted them to see one more miracle, that being the splitting of the sea. Not just the splitting of the sea, but the craziness that after witnessing the splitting of the sea (and all that he had done before that up until then), they still had the idea that they should follow the Jews through the sea.
Were they crazy? What were the Egyptians thinking after all that they had been through? How could they not realize that they were about to be decimated? When would they decide they had had enough? It could only be because Hashem hardened their hearts and caused them to forget all that had happened already. But why do all this?
I think Hashem is just letting everybody know there is a new guy on the block. Don't pick on the Jews. I've got their back. However you want to put it, Hashem was telling the nations of the world that these are not people to be messed with. By totally destroying them time after time with miracle after miracle, this extra event was like putting an exclamation point on the Exodus.
Don't mess with the Jews. Gods got my back.