"Each one went straight ahead. Wherever the spirit would go, they would go, without turning as they went." NIV translation
The creatures are in tune with the very Spirit of God and focus on going straight to where He desires. We, too, can follow the Spirit in such a manner if we choose to listen and obey.
"The appearance of the living creatures was like burning coals of fire or like torches. Fire moved back and forth among the creatures; it was bright, and lightning flashed out of it. The creatures sped back and forth like flashes of lightning." NIV translation
The creatures are like royal heralds who went before a king to announce his coming presence. Those heralds would blow trumpets but trumpets are not necessary because God is light and a consuming fire, that is what it looks like when He is around. Because God cannot be contained, the light flashes out like lightning. These creatures are so in tune with God that they immediately go in the direction of God's will and so it looks like flashes of lightning.
"As I looked at the living creatures, I saw a wheel on the ground beside each creature with its four faces. This was the appearance and structure of the wheels: They sparkled like chrysolite, and all four looked alike. Each appeared to be made like a wheel intersecting a wheel." NIV translation
Now, Ezekiel begins to describe the wheels but they are not your ordinary wheels. They looked like a wheel inside a wheel but we do not know why. Each creature had his own wheel but they all worked together.
"As they moved, they would go in any one of the four directions the creatures faced; the wheels did not turn about as the creatures went. Their rims were high and awesome, and all four rims were full of eyes all around." NIV translation
Eyes are a symbol of knowledge throughout the Bible and the eyes on the wheels remind us that they have an intelligent purpose. They do not swerve from that purpose but follow the direction of the creatures. God has a purpose for all things and, through the direction of the Holy Spirit, we can also be unswerving in our pursuit of what He has for us.