I can see what Snyder means saying that this is going to be the most realistic of his movies.
He just means that the world around Superman is going to be very realistic. Not over-stylized as hes previous works. And I think thats the right direction to go for.
A realistic world, like ours, makes Superman more.. well.. Super. We see a world we are very familiar with, and this amazing person with incredible abilities. Its easier relates with.
In an stylized world, everything would just looks fake. "Oh, sure, someone so powerful in a fantastic world" kind of thing. But grounded in reality, it makes Superman shines.