‘In the first year of Darius, the son of Ahasuerus, of the seed of the Medes, who was made king over the realm of the Chaldeans, in the first year of his reign, I, Daniel, understood by the books the number of years about which the word of YHWH came to Jeremiah the prophet for the bringing to conclusion of the desolations of Jerusalem, even seventy years.'
For Darius the Mede see chapter 6 opening. Here he is called the son of Ahasuerus (Persian khshayarsha). This was a name applied to royalty (the Greek equivalent is Xerxes) in the Medo-Persian empire and there is no reason why someone with such a name should not be father to Darius the Mede. And he is said to be ‘of the seed of the Medes'. This stresses that ‘the Mede' refers to his birth and not to the empire over which he was king.
‘Was made king over the realm of the Chaldeans.' ‘Was made.' He was acting as an under-king to the ruler of the whole empire. We only hear of the first year of his reign and it may well be that he died, or was replaced, shortly after, for within two years Daniel begins to date in terms of Cyrus (Daniel 10:1), whose son took over the governorship of Babylon. As Darius was 62 years old when he was ‘made king' (Daniel 5:31) he would not rule for long, and he was probably appointed as having a recognised ability for the organisation of administrators (Daniel 6:2). Nothing is known of him historically, but in view of his short tenure this is not necessarily surprising. He has been variously identified with Cyrus himself, and with Cyrus' general Gobryas, but his age at accession makes these identifications unlikely. There is no good to reason to deny his historicity, or for not accepting his identity at face value.
‘Understood by the books.' Daniel clearly had a number of ‘books' which included at least a part of the prophet Jeremiah (see Jeremiah 36:2-3; Jeremiah 36:28). It is very possible that he had other parts of the Old Testament as well, especially Deuteronomy. These told him that Jerusalem's period of barrenness and emptiness was to be seventy years, after which His people would return to the city (Jeremiah 25:11-14; Jeremiah 29:10-11; compare 2 Chronicles 36:21). The prayer that follows is clearly based on Scripture and confirms that Daniel was heavily influenced by Jeremiah and Deuteronomy, even to the use of the divine name YHWH, which is found nowhere else in Daniel.
‘Seventy years' would be considered a round number indicating the divine perfection of the period involved and a fairly long period, thinking in terms of a lifetime (Psalms 90:10). Daniel at this stage had been in Babylon since 605 BC (sixty six years) and was thus probably around eighty. He would therefore have felt that God's time was surely near.