How is God's rest on the 7th day traditionally understood?

I think God's resting on the seventh day was in part to give us an example to follow.

It will be a sign between me and the Israelites forever, for in six days the LORD made the heavens and the earth, and on the seventh day he abstained from work and rested. - Exodus 3:17, NIV

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.

but during the seventh year let the land lie unplowed and unused. Then the poor among your people may get food from it, and the wild animals may eat what they leave. Do the same with your vineyard and your olive grove. - Exodus 23:11, NIV

As Israel matured, it forgot about giving the fields a rest every seventh year. Eventually, it caught up to them.

The land enjoyed its sabbath rests; all the time of its desolation it rested, until the seventy years were completed in fulfillment of the word of the LORD spoken by Jeremiah. - 2 Chronicles 36:21, NIV

In a sense, Jesus settled this issue with His words in Mark 2:27, where He said,

"'The Sabbath was made for man, and not man for the Sabbath.'"

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.

The interpretation of verse doesn’t say God “needed” to rest; but that God stopped His acts of creation on the seventh day.

Genesis 2:2 And on the seventh day God finished his work that he had done, and he rested on the seventh day from all his work that he had done.

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:

'Below the firmament, whose grounding I have made firm,
A house I shall build, let it be the abode of my pleasure.
Within it I shall establish its holy place,
I shall appoint my holy chambers, I shall establish my kingship'
  (*Enuma Elish* 5.121-124).

'We will make a shrine, whose name will be a byword,
your chamber that shall be our stopping place, we shall find rest therein'
  (*Enuma Elish* 6.51-52).

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:

'Let us go to his dwelling-place;
let us worship at his footstool.'
Rise up, O Lord, and go to your resting-place,
you and the ark of your might. 
Let your priests be clothed with righteousness,
and let your faithful shout for joy. 
For your servant David's sake
do not turn away the face of your anointed one. 
The Lord swore to David a sure oath
from which he will not turn back:
'One of the sons of your body
I will set on your throne. 
If your sons keep my covenant
and my decrees that I shall teach them,
their sons also, for evermore,
shall sit on your throne.' 
For the Lord has chosen Zion;
he has desired it for his habitation: 
'This is my resting-place for ever;
here I will reside, for I have desired it.'
  (Psalm 132.7-14, NRSV translation)

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'.

Resources

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.

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.