"When the living creatures moved, the wheels beside them moved; and when the living creatures rose from the ground, the wheels also rose. Wherever the spirit would go, they would go, and the wheels would rise along with them, because the spirit of the living creatures was in the wheels." NIV translation
The creatures were in tune with God and controlled the wheels. They had a spirit of complete obedience to God and that spirit was also in the wheels. The wheels knew their purpose, remained focused on that, and simply obeyed. We can learn much for our walk with the Lord from these wheels. God has given each of us a purpose and His presence will be there with us in the form of the Spirit. If we remain focused on our purpose and tuned in to the Spirit, He can and will work through us for His glory.
This verse basically repeats the previous passage and anytime something is repeated in the Bible it reminds us that we really need to take notice. This verse reminds us that the wheels did not move first but waited on the movement of the creatures. That is a good lesson for us in our walk with the Lord. Many times we get ahead of God's timing and may be doing what God wants us to do but it may not yet be the appointed time. We must pray and wait for the guidance of the Spirit and only move when the Spirit moves us.
"Spread out above the heads of the living creatures was what looked like an expanse, sparkling like ice, and awesome." NIV translation
This description is very similar to John's description of the throne in heaven (see Revelation 4) and the sea of glass. This is a reminder that they are sent from heaven by God.
"Under the expanse their wings were stretched out one toward the other, and each had two wings covering its body." NIV translation
This description is a lot like the description of the cherubim that were a part of the atonement cover on the ark of the covenant (see Exodus 25). Their wings were stretched out to cover the ark and God would be in their presence.