By the seventh day God had finished the work he had been doing; so on the seventh day he rested from all his work. And God blessed the seventh day and made it holy, because on it he rested from all the work of creating that he had done. Genesis 2:2-3
God did not need to rest after a full week of work like we do.
"Rested" is the Hebrew word shabath which we get our word sabbath. There are a number of different meanings for the word, but the closest word that applies here is "ceased from work." God stopped creating. He had created all he needed to create and everything that was once "formless" and "empty" was now filled.
God doesn't get exhausted. We do. God made the day holy so we would stop working and set the day aside in remembrance of everything he created for us.