And God blessed them, and said to them, "Be fruitful and multiply. Fill the earth and subdue it: have dominion over the fish of the sea, and over the birds of the air, and over every living thing that moves upon the earth.
And God said, "Behold, I have given you every plant that bears seed upon the face of all the earth, and every tree that has seed-bearing fruit, for food.
And to every beast of the earth, and to every bird of the air, and to every thing that creeps upon the earth, having the breath of life, I have given every green plant for food" and it was so. (Genesis 1:28-30)
God set up humanity to understand other creatures and care for them. We call the animals by name, just as the Lord calls us by name. (As per the quote above, the book of Genesis says that in paradise, humans may have "ruled over" the animals but were not to eat them.)
Seen in this way, Eden is a template for how we should fill the earth and subdue it. God's establishment of paradise is an action that he calls us to continue, where he intends for us to walk in his footsteps. Later models of "subduing" things were corrupted by sin. But the right kind of rule makes things flourish and prosper, being better than before. The right way to "fill the earth and subdue it" would turn the whole earth into a paradise, keeping to the pattern that God showed.