This is really the only scene that gives insight into Duncan's nature. He does have lines upon his arrival at Macbeth's castle, but these words are part of a very conventionally polite exchange and can't really be said to reveal much that is personal about Duncan's nature. Act I, scene iv, however, gives insight into Duncan's perspective.
At the top of the scene, when he is told of how the rebellious Thane of Cawdor died, he simply says:
There's no art
To find the mind's construction in the face.
He was a gentleman on whom I built
An absolute trust.
The image here is of attempting to understand the mind of a man by his outward actions. Duncan believes that this is not possible and admits that he mistakenly "built/An absolute trust" on the now dead Thane of Cawdor. This suggests that Duncan is not the best judge of a man's character.
This is the exact moment at which Macbeth enters the scene, having just been told by the witches that he will be king. The rest of the scene, then, is one in which Duncan's lines are full of dramatic irony, since the audience has the information of the prophesy that Duncan does not.
Following are some of the images from Duncan's lines that stand out in this scene.
. . .thou art so far before
That swiftest wing of recompense is slow
To overtake thee.
This line comments on Macbeth's speed and suggests that paying him back for all he has done in support of Duncan is like a bird ("swiftest wing") that cannot catch up to Macbeth.
I have begun to plant thee and will labour
To make thee grow.
This line suggests that Duncan sees Macbeth as his protegee, and like a good father-figure or gardener, he will tend Macbeth's development to see him arrive at his full fruition.
. . .he is full so valiant,
And in his commendations I am fed.
It is a banquet to me.
These words, again, refer to Macbeth. Duncan compares the excellent qualities possessed by Macbeth to food that, rather than feeding Macbeth, feed him. He alludes to how many qualities by referring to their sum as "a banquet."
For more on Duncan and this scene, please follow the links below.