The word 'understanding' here in Hebrew is 'ruwach', which can mean 'scent, sense/smell, perception, anticipation'. In other words, being of 'quick understanding' is being 'quick-scented, quick in sensing/smelling, quick in perception, or quick in anticipation'. Interestingly, this word 'ruwach' is the same word found in Genesis 1:2 that says, '...And the Spirit ('ruwach') of God moved upon the face of the waters'. Here, this same word 'ruwach' means 'spirit, breath, or life'.
Let's look at Isaiah chapter 11 now. This chapter speaks about our Savior Jesus, the Messiah who was to come. Isaiah 11:1-2 begins with, 'And there shall come forth a rod out of the stem of Jesse, and a Branch shall grow out of his roots. And the spirit of the Lord shall rest upon him, the spirit of wisdom and understanding, the spirit of counsel and might, the spirit of knowledge and of the fear of the Lord'. And it's from here that Isaiah 11:3 continues, 'And shall make him of quick understanding in the fear of the Lord...'
As you can see, all the above attributes, i.e. wisdom and understanding, counsel and might, knowledge and the fear of the Lord, and of course, being of 'quick understanding' in the fear of the Lord are attributes found in Him. And you know what? The Bible says 'as He is, so are you in this world'! (1 John 4:17) Receive the impartation of all these in your life by faith now!
In this end-time, God is also raising a people who are like Jesus, a people who are of 'quick understanding', a people who are spiritually-sensitive (to the things or situation in and around them), and a people who just know how to make a way of escape when they sense danger (or something amiss)! One example is in Luke 4:30. Here, even in the midst of 'danger' surrounding Him (and when some people were trying to kill Him), He just knew how to make a way out - somehow, someway, supernaturally! And He knew His time (to die) was not yet.
I like the definition 'quick-scented' in the first paragraph. The word 'scent' is defined in Oxford Dictionary as 'characteristic smell of something, particular type of smell, smell left behind by a living thing that allows others to track/follow, feeling of the presence of something, or discovering something by sense of smell'. Therefore, I can also say being 'quick-scented' means 'when you sense/smell something, you just know what it is or what is going on'.
Today, the Lord is indeed sensitizing (or 'scent-sitizing') His people to be likewise, a people who are enabled by His Spirit to sense and move with His timing and season (being sensitive to every change or movement in the spiritual realm, and what He is currently doing in the spiritual realm at the moment).
In fact, what is in the spiritual realm is reflected by the physical realm. In the animal kingdom, there are animals which are very sensitive even in the most ‘minute’ of any earth movement. One of the earliest recorded instance of animals being able to sense impending earth movements/earthquakes was recorded in the history of the Greek. During the winter of 373 BC, ‘all the mice, beetles, centipedes, and every other creatures of that kind in the city of Helike left’. After these creatures left, an earthquake occurred, the city went under, an immense wave flooded, and Helike disappeared!
More recently, it has been recorded that before a powerful earthquake hit Chile in 2010, dozens of deep-sea fish surfaced and was discovered by a group of Japanese fishermen. Shortly before the 2011 earthquake and tsunami in Japan, a number of deep-sea fish were found stranded on beaches nearby. In a scientific study of earthquakes, waves, and earth movement by a Japanese specialist in ecological seismology, it has been found out that “deep-sea fish living near the sea bottom are more sensitive to the movement of active faults than those near the surface of the sea.” In the spiritual realm, the same is also true, that the deeper one’s walk with God, the more likely he/she’s going to ‘catch’ or sense what’s currently going on in the spiritual world!
Sensing/smelling has to do with inhaling/breathing in. In Genesis 2:7, the Bible says, 'And the Lord God formed man of the dust of the ground, and breathed (out) into his nostrils the breath of life; and man became a living being'. This word 'breathed (out)' is 'naphach' in Hebrew, which can mean 'blow, scatter (as in scattering seeds), kindle, give up'. Genesis 1:26-27 says you are created after His own image and likeness. In other words, you are made after His kind, i.e. His seed (that He scattered). And even when man sinned, He sent His only Son to 'give up' His Spirit at the cross (John 19:30), so that we have His Spirit (breath, life) again. His redemptive work for mankind!