The doubling of words and expressions like this is a type of idiomatic expression in Hebrew. It usually means that something is applied to each item or individual of a listed series. In the case you are bringing, it is applied to the Princes of the tribes. By doubling this expression, it means that one Prince from the series will bring an offering for each of the days. The literal translation does not effectively convey the meaning of the Hebrew original.
The same idea can be seen in the details of the preparation of the incense recited in morning blessings and also found in Keritot 6a. It can also be found dealing with the bread offering for Shabbat in VaYikra 24:8.
There are places in Midrash and in Kabbalistic literature which use the doubling of certain phrases as a departure point for commentary. But the usual and most common usage is in the fashion described above.