From a non-religious view, God represents everything not in your control. You thank God for e.g. not having you or your guardian/provider be fired/laid-off or otherwise yourselves being put in a position where you can't eat (illness, etc.).

The person who cooked your meal isn't the only one responsible for your being able to eat. They need the ingredients and efforts of everyone making such ingredients and putting them in your home as well as luck for nothing going wrong (transportation, good harvest, etc.), generally most of it "by the will of God" / "under God's control" (i.e. outside of your control).

In Spanish, a maybe more common and culture-specific expression may be "Provecho" which is said to others about to eat (or that are currently eating and you're in the process of greeting). It means "benefit"/"utility" and is said in hope that the food is of usefulness to the health and well-being of the person(s) about to eat / currently eating.