Thank you for making me look this up.
(Quoting from the Siddur Vilna)
The Avudraham says that it is a zecher to Yetzias Mitzrayim.
The Machzor Vitri says that we say it because it was a custom in the Jewish communities of Rome, Spain, and those surrounding them, from the day we were exiled from Jerusalem until now, to sing it all year every day, and “Minhag avoseinu Torah hee”.
Also, we say this Shira which is about the fall of our enemies, and to praise the One Who does wonders, and to bless His name before and afer these praises (Baruch Sheamar and Yishtabach.)
Hope this helps!