How is God's rest on the 7th day traditionally understood? It seems that, to an omnipotent and omnipresent being, the concept of rest would be academic. Why did God rest then? How is this traditionally understood? What would have happened if he hadn't rested?
As you imply, God did not need to rest. But He chose to, apparently as a pattern for us:

Exodus 20:8-11
“Remember the Sabbath day by keeping it holy. Six days you shall labor and do all your work, but the seventh day is a sabbath to the LORD your God. On it you shall not do any work, neither you, nor your son or daughter, nor your male or female servant, nor your animals, nor any foreigner residing in your towns. For in six days the LORD made the heavens and the earth, the sea, and all that is in them, but he rested on the seventh day. Therefore the LORD blessed the Sabbath day and made it holy.

This is not the only time God has done something He didn't need to, to set an example for us. Another was when Jesus was baptised (Matthew 3:13-15).