James Stalker insightfully brings out some key reasons why Jesus used illustrations so much in His preaching:
But the discourses of Jesus had a still more popular quality: they were plentifully adorned with illustrations. This is the most attractive quality of human speech. The same God being the Author of both the world of mind and the world of matter, He has so fashioned them that the objects of nature, if presented in a certain way, become mirrors in which are reflected the truths of the spirit; and we are so constituted that we never relish truth so well as when it is presented in this way. Nature contains thousands of these mirrors for exhibiting spiritual truth which have never yet been used but await the hands of the masters of speech who are yet to be born.
Christ used this method of illustrating truth so constantly that the common objects of the country in which He resided are seen more perfectly in His words than in all the historians of the time. . . .
It was because Jesus had exquisite love and consideration for His hearers that He thus sought out acceptable words to win their minds. But there was a reason in Himself besides. It is when the mind of a preacher is acting on the truth with intense energy and delight that it coruscates in such gleams of illustration When the mental energy is only smouldering in a lukewarm way inside the subject, then you have the commonplace, prosaic statement; when the warmth increases and pervades the whole, you get the clear, strong, impressive statement; but, when the glow has thoroughly mastered the mass and flames all over it, then comes the gorgeous images and parables which dwell for ever in the minds of the hearers.
—The Example of Jesus Christ: Imago Christi, 186-188