‘When they went they went on their four sides. They turned not as they went. But to the place where the head looked, they followed it. They turned not as they went.'
The fours sides would be north, south, east and west, and when they moved they moved directly forward without being diverted. Thus they had freedom of travel and a certain inevitability about their progress. Nothing could frustrate their purpose. This latter is emphasised by being mentioned twice.
And they went where the head (or chief) looked. This may refer to ‘the cherub', the anointed one, as chief among them, or to the heads of each of the cherubim (compare Ezekiel 10:14 and Ezekiel 10:16), depending on whether we see the ‘they' as being the wheels (Ezekiel 10:10) or the cherubim (Ezekiel 10:12). Or it may even refer to the head of Yahweh on His throne. He had only to look and they went where He looked.