When you oxidize something you are removing electrons
When you reduce something you're adding electrons
So the one that is gaining electrons is oxidizing the other substance by taking away relectrons from it and the one losing electrons is reducing the other substance by adding electrons to it.
You can figure out which is which by looking at the charge of each substance
Mg has a charge of 2+ because it had 2 electrons in its outer shell which it will lose to have a full outer shell.
I has a charge of -1 because it has 7 electrons in its outer shell and it gains 1 to have a full outer shell.
Mg is giving electrons to I so it's reducing it and is the reducing agent
I is taking electrons from Mg so it's oxidizing it and is the oxidizing agent.