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:
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).
God resting on the seventh day is not an indication that He was "tired" or somehow needed rest, but is just a way of expressing that He had completed His work of creation.
Many (probably mainly old earth creationists) believe that we are now living in that "seventh day", since the Genesis account never says the seventh day ended (as it does with the other 6 days). In this view, clearly God is not resting, in the sense of doing nothing--He is still active throughout human history, including the work of sending Christ, etc. He is simply resting from the work of creation.
The interpretation of verse doesn’t say God “needed” to rest; but that God stopped His acts of creation on the seventh day.
The Hebrew word “u•ishbth” when translated has one of the main definitions as “to cease or stop.” So the understanding is that God “stopped” His work; He “ceased” creating on the seventh day.
When God said, “Let there be light,” the light appeared. He simply spoke creation into existence. Throughout, Bible depicts God as omnipotent—He has all power— and it doesn’t make much sense that He would need to “rest.” That is not the intended meaning of this verse or the word.
Because God ceased from work that day, the Israelites were to cease from their work on the Sabbath.
My answer here is an adaptation of part of my answer to a related question on Hermeneutics.SE:
The purpose of 'rest'
In two of his books (listed below), John H. Walton examines Genesis 1.1-2.3 according to its similarities to other 'creation myths' in the ancient near east (ANE from here onward), verbal cues with contemporary or related Hebrew scriptures, and so on. One of the two main purposes of the text of Genesis 1 can once more be determined by verbal cues and literary parallels to other ANE creation myths.
Walton notes that the Babylonian creation myth, the Enuma Elish shows the world and humanity being created, and concludes with the creation of a temple for the god Marduk:
The climax of the creation of the world was the creation of a temple, which would serve as the place of 'rest' for the supreme god-king Marduk.
Genesis 2.2-3 describes day seven of the creation 'week'. At this point, 'the heavens and the earth were finished' already, so day seven is not an act of creating anything. Instead, day seven gives meaning to what has just been created: God comes to 'rest'.
Appealing to other Hebrew texts, Walton states that 'divine rest' in ANE thought always occurs in a temple. One key biblical text that substantiates this claim is Psalm 132.7-14:
Various points in this passage make it abundantly clear the author is describing the temple in Jerusalem: it houses the ark of the covenant, it has priests, it has a connection to David, and is located in Zion. And it calls the Jerusalem temple the 'dwelling-place' and 'resting-place' of God; God 'dwelled' and 'rested' in his temple.
This is simply how the ancient world perceived 'divine rest'.
Why did God rest on the seventh day? Because he was settling into his newly-constructed home. The picture of God 'resting' on the seventh day within the context of Genesis 1 tells us that the universe he had just created was intended to function as his 'temple', with humanity as the temple icon, reflecting his image (i.e. 'the image of God') into that 'temple'.
John H. Walton, Ancient Near Eastern Thought and the Old Testament: Introducing the Conceptual World of the Hebrew Bible.
John H. Walton, The Lost World of Genesis One.
I think God's resting on the seventh day was in part to give us an example to follow.
It is interesting to note that research over the years has shown that we human beings need time to rest and re-create. We are not created to go full-out, 24/7. The psychological literature often talks about taking breaks as a good way to reduce stress. Taking time to rest gives our body time to re-create itself. Even in weight training and body building the concept of rest appears: don't work the same muscle group every day (Weight Training 101).
Our minds also need time to rest. For many people, just setting aside a difficult problem is the key to finding the answer.
It's interesting to consider that by setting aside a special, Holy day for God, we also are given a chance to recreate ourselves in His image. It gives us a day to stop, and be washed by the water of the Word. It gives us a chance to see things in God's perspective, not our own limited view.
Another interesting thing is to look at the variations in the theme of 7 periods of rest.
This theme of rest in terms of groups of seven is not limited to just a Sabboth rest. It also is found in the ancient rules for planting fields.
As Israel matured, it forgot about giving the fields a rest every seventh year. Eventually, it caught up to them.
In a sense, Jesus settled this issue with His words in Mark 2:27, where He said,
The reason for God's "resting" on the seventh day of creation was for our benefit, not His. He set a pattern for us to follow by giving us the command to work for six days and rest for one.
As important as work is, it is not the end-all and be-all of life. We need to seek balance in all things, and to set aside time to worship God within a local assembly of believers is not only a key part of our service of worship but it an important means of having our spiritual batteries recharged for the week ahead. On Sunday, the traditional day many Christians "go to church," ever since Christ's resurrection on the first day of the week, we give back to God by singing His praises and celebrating His faithfulness and goodness during the past week, and we receive the strength to enter a new week with renewed spiritual vigor for doing God's will, individually and corporately.
To "work" on the seventh/first day is not a sin, as Jesus pointed out. He, being Lord of the Sabbath, put His imprimatur on "doing good" on the Sabbath (see Matthew 12, Mark 2, and Luke 6). That good could very well involve working for wages, on the one hand, or helping a brother or sister in Christ to move into a new apartment, on the other. However, as soon as we start to neglect to our own hurt and the hurt of others the gathering of ourselves together in a local fellowship, we risk losing that balance which God desires for all of us.