Daniel 10:12 He said to me, 'Do not fear, Daniel, for from the first day that you set your heart to understand, and to fast before your G-d, your words have been heard, and I came because of your words.  13 But the heavenly prince of the Persian kingdom stood opposed to me for twenty-one days, when, behold!  Michael, one of the foremost heavenly princes, came to help me, and I remained there beside the kings of Persia.
13. But the heavenly prince of the Persian kingdom. [I.e., the angel appointed as caretaker of the affairs of Persia.]
Stood opposed to me [lit. was standing against me.]  The heavenly prince of the Persian kingdom had been petitioning for additional longevity for his proteges throughout these 21 days and I have been fighting his petition (Rashi).
[It stands to reason that these 21 days, are identical with the 21 days of Daniel's mourning (above vs. 2).  It follows that here, too, years are meant.  Hence, this vision took place not in the third year of Cyrus, but during the rule of Darius the Persian (see above vs. 2).  The angel was imparting to Daniel that these 21 years (the fall of Babylon, the start of reconstruction of the Temple in the first year of Cyrus's reign, the subsequent revocation of Cyrus's edict, and the renewed construction of the Temple at the time the angel was speaking) were due to the relative position of the angels assigned to the respective nations, not to the apparent political causes.]
Of the foremost heavenly princes.  I.e., one of the most eminent of the angels (Rashi).
[In the heavenly tribunal, Michael is prince of Yisrael, as seen in vs. 21 (Michael your heavenly prince).  Ramban (VaYikra 18:28), however, differentiates between Michael and the other angels cast in the position of heavenly princes.  Whereas the other angelic princes actually have hegemony over their charges, Yisrael's prince is different because "Hashem's portion is His People"  (Devarim 32:9), unlike the other nations who are under the guidance and rule of their heavenly prince.  This is what Moshe means when he admonishes Yisrael:  "Take heed unto yourselves...lest you lift up your eyes, and see...all the host of heaven...which Hashem your G-d has allotted unto all the peoples under the whole heaven.  You, however, Hashem has taken" (Devarim 4:15-20)  Therefore, Michael's role is only that of an advocate for his People, which role he filled perfectly, as seen in this verse.]
And I remained there.  To counteract the petitions of the heavenly prince of the Persian kingdom (Rashi).
[This is a recapitulation of what the angel has told Dani'el up to now.]
Malbim sees this as prophetic symbolism representing the welfare of the Jews from that time on in the Persian empire.  I remained - i.e., my influence is now acknowledged by the heavenly prince of the Persian kingdom. [Artscroll Tanach Series - Daniel]