Here is a good summary of the need of Extemporary preaching from Exiled Preacher.

Here are some thoughts on preaching without notes. I started to preach in this way many years ago for a number of reasons. First, I tend to gesticulate a bit while preaching. Once I knocked my notes out of the pulpit and had to retrieve them mid-sermon, which was a bit embarrassing. Second, I sometimes used to find a new vein of thought opening up while preaching. I would go with this, but run ahead of my notes. When the moment of inspiration dried up, I would have to pause for what seemed to me like an eternity, to find my place in the sermon.
So, one day I tried preaching without notes. I did my usual preparation, prayed hard and decided to give it a go. As an insurance policy, I brought my sermon with me into the pulpit, just in case it all went horribly wrong. I felt liberated and didn’t need to glance at my notes once. Next time, I prayed even harder and left the notes at home. I found that I was able to keep to my prepared sermon outline, but be more spontaneous in my preaching. This was about 18 years ago, when I was in my 20’s.
Extemporary preaching does not mean speaking without diligent sermon preparation. This kind of speaking must not be at the expense of considered Biblical exegesis, clear and logical ordering of the material and thought given to matters of illustration and application. Preaching without notes demands a clear, straightforward sermon structure, because the preacher himself will not be able to remember an overly elaborate address. Three or four main points with their attendant sub-points will be the preacher’s guide as he delivers his message. The preaching may develop in unexpected ways, but any improvisation will generally take place within the basic framework of the sermon.
An extemporary preacher should not seek to commit his whole sermon to memory. A prayerful and meditative reading of notes prior to preaching should be enough to impress the burden of the message on the mind and heart of the speaker. To be tied to a memorised recitation of a message is as restrictive as preaching from notes.
The big advantage of preaching without notes is increased interaction with the congregation. Eye contact can be maintained so that the preacher may react to the response of the people to his message. If someone looks a bit confused, the preacher can clarify his point. If some seem to be really helped by something, the preacher can elaborate on his exposition and seek apply the truth for the good of the people. If he is loosing the congregation, an illustration or maybe a provocative statement will regain their attention. Hopefully, the people will feel that the preacher is speaking to them rather than at them as this rapport develops during the message.
Extemporary preaching is not without its difficulties. It can leave you feeling exposed and vulnerable. There is nowhere to hide. You cannot bury your head in your notes and steam on ahead when things aren’t going well. It is a risky business that demands faith in God. Because you will not have prepared the exact words you are going to say beforehand, care must be taken not to slip into the same old stock phrases and cliches. Those who do not use notes in preaching should not draw attention to the fact before the congregation like a child saying ‘look no hands’ when letting go of the handlebars of his bike. Kids who do that often fall off! The Bible-centred content, not the style of preaching is what matters.
Not all preachers are able to speak in this way. We should work with the gifts that God has given us. Jonathan Edwards famously read his sermons with great effect. But I believe that he determined to be less dependent on his notes after hearing George Whitefield’s extemporary preaching. Whether we use no notes, few notes or lots of notes, Christ-exalting, Spirit enpowered preaching must be our aim, even if we often (or always) fall short of that goal.
Sometimes it may be necessary for mainly extemporary preachers to use some notes. When I was preaching on Daniel a few years ago, I had to use some notes for chapter 11. I couldn’t get through all those verses about the northern and southern kings and queens of Greece without something on paper. I often use some notes for our discussional Bible studies too, as Bible study is different to preaching. Theological or historical lectures demand pretty full notes, but again, lecturing should be different to preaching.
Nothing is more exhilarating than preaching the gospel with freedom and spontaneity. Preaching without notes does not guarantee this sense of liberty, but perhaps, in the goodness of God, it may help.
see also www.disciplemaking.net