I have always interpreted Daniel 12:4 simply by the plain reading of the text. Of course we can not gain understanding of one simple passage unless we read it with the surrounding texts so we have to look at the surrounding passages to give clarity to this one verse. Daniel 12:1-4 tells us of a time when Michael the Archangel will stand up for the people of Israel and then there will be time of trouble (The Tribulation Week). It also talks of those who are dead coming to life, and the righteous (wise) will live forever. This leads up to probably a very puzzled look on Daniel’s face. Throughout the entire book of Daniel, we see God blessing Daniel through many dreams and revelations. Many of these dreams and revelations are revealed to Daniel complete with interpretation, but many of them Daniel remained puzzled with. In fact sometimes Daniel is even more puzzled once the interpretation is given. This is significant because many of Daniel’s revelations come with the caveat of ‘the end shall be’ (Daniel 8:19), or ‘the time of the end’ (Daniel 12:4; Daniel 12:9) or at least have an implication of last things as we find in Daniel 2:44 or Daniel 7:27. With all these things in mind, and when I look at the Hebrew in the text of Daniel 12:4 I read it quite simply as the following (paraphrasing):
“But you Daniel, write down what you have seen. Seal these revelations up in a book until the time of the end, where people will have greater understanding. For their knowledge will increase and their time will be marked by this increase in knowledge and travel throughout the world.”
Historically travel was associated with knowledge. Without the internet, the Discovery Channel and National Geographic, one had to travel to learn more about the world around us. We learned through dialog with people from other nations, and we shared our knowledge and technologies with each other through trade and commerce. Daniel could not have foreseen our world as it is now, nor could he have understood it, but it might have made sense that people would gain knowledge by moving to and fro.
Regardless, God was letting Daniel know not to worry, but simply be the scribe and write it down and keep it safe. These prophecies were for a later time and God’s people would discern them in due time. The words, ‘go your way’ must have been a relief for Daniel as a release to then continue in service at his time, and not worry about these things of a future time. This same decree is echoed in Daniel 12:9 which leads us to your next question.