Father Seraphim Rose of blessed memory's Icon corner. Picture taken in his hand made cell.
Why a corner, or is that just a clever term?
I'm very surprised no one gave a proper answer for this question. It is often located in a corner to eliminate worldly distractions and allow prayer to be more concentrated. If it's in a corner (preferably an east corner) it takes away your sense of direction and and helps you focus. You can think the Church Fathers and there wisdom for this.
What is traditionally present? There are a ton of variations in pictures.
Icons of Christ, the Theotokos, and the Patron Saint. An oil lamp normally hangs in front of the icons. The careful trimming of the lamp to keep it burning at all times is interpreted as symbolic of the attentive daily care faithful Christians should take over their souls. Relics of saints (if the family possesses any) and a Gospel Book and a blessing cross would be kept there, as well as incense, holy water, palms and pussywillow from Palm Sunday, candles from Pascha (Easter), and other sacred items, as well as a personal Commemoration Book (containing the names of family and loved ones, both living and departed, to be remembered in prayer).
What is their primary purpose?
The Book of Acts and the Epistles of the Apostle Paul record that in the early Church, Christians used to meet in the homes of the faithful. (Acts 2:46, Acts 20:7-12, I_Corinthians 16:19, etc.) This tradition of the "House Church" continues to this day in Eastern Christianity. The home is considered to be a microcosm of the Church. The parents (both the husband and the wife) are the "clergy" of the house church, and the children are the "laity." The wedding ceremony ("crowning") is analogous to Ordination, and the house is blessed with a rite that is based upon the Consecration of a Church. Once a year, the priest will come to bless the house with Theophany Water.
An Orthodox Christian is expected to pray constantly. According to Bishop Kallistos Ware, "In Orthodox spirituality, there is no separation between liturgy and private devotion." Thus the house, just like the Temple (church building), is considered to be a consecrated place, and the center of worship in the house is the icon corner.
Is it something that should be vetted and blessed by your priest?
Again as stated above, "Once a year, the priest will come to bless the house with Theophany Water." If you can't wait that long, take your icons to church and have them blessed. Some people also have their incense blessed because we cense our homes, the demons don't like it and flee from the smoke. (Remember, one you bless an icon it belongs to the Church and is property of God. You don't not through them away. If you have old icons, give them to the priest and they will be burned with a prayer said.)
Is there an area of the home that is preferred?
Ideally, the icon corner is located so that it is visible when one first enters the house from the main entrance. Traditionally, when first entering the house, an Orthodox Christian would venerate the icons before greeting the members of the house.
Is N,S,E,W an issue?
An icon corner is normally oriented to face east. That's because the bible mentions when Christ comes again during his second glorious coming, He will be seen in the East. So we pray facing east to always be mindful of the second coming. If you notice, most (if not all) Orthodox Churches face east.
Are the icon choices personal or is there a specific order?
They are mostly personal choices. I picked icons of parables that I relate to and I have Saints that I wish to pray for me or whom I relate to because of how they lived (better then I of course) and ask for there strength and help to get over a certain temptation or sin. I'm looking to a monastic path in life so I have a lot of monastic saints. There are lots of different icons of Christ and the Theotokos that have different meaning and some are copies of miracle working icons. Just pick the icons that have special meaning to you.
Normally you won't have icons of Elders who are alive or who haven't been recognized as saints yet. Ask your priest about this. en.wikipedia.org/wiki/Icon_corner