Wherefore they called these days Purim after the name of Pur. Therefore for all the words of this letter, and of that which they had seen concerning this matter, and which had come unto them,

And since that time these days are called Phurim, that is, of lots: because Phur, that is, the lot, was cast into the urn. And all things that were done, are contained in the volume of this epistle, that is, of this book:

Therefore they called these days Purim after the name of Pur. Therefore, according to all the words of this letter, and for what they had seen concerning this matter and what had happened to them,

therefore they have called these days Purim, by the name of the lot, therefore, because of all the words of this letter, and what they have seen concerning this, and what hath come unto them,

Why they called these days Purim after the name of Pur. Therefore for all the words of this letter, and of that which they had seen concerning this matter, and which had come to them,

So these days were named Purim, after the name of Pur. And so, because of the words of this letter, and of what they had seen in connection with this business, and what had come to them,

They called these days Purim - That is from pari, the lot; because, as we have seen, Haman cast lots to find what month, and what day of the month, would be the most favorable for the accomplishment of his bloody designs against the Jews. See on Esther 3:7 (note).
And of that which they had seen - The first letter to which this second refers, must be that sent by Mordecai himself. See Esther 9:20.

Wherefore they called these days Purim, after the name of Pur,.... The lot; because of the lots cast by Haman; see Esther 3:7,
therefore for all the words of this letter; in obedience to what Mordecai wrote in his letter to the Jews, and because of the things contained in it:
and of that which they had seen concerning this matter; with their own eyes, in the several provinces where their enemies rose up to assault them, but were destroyed by them:
and what had come unto them: by report; as the fall of Haman, and advancement of Mordecai, and the favours shown to Esther and her people; all this belongs to the following verse, containing the reasons of the Jews' appointment and engagement to observe the days of Purim.

they called these days Purim after the name of Pur--"Pur," in the Persian language, signifies "lot"; and the feast of Purim, or lots, has a reference to the time having been pitched upon by Haman through the decision of the lot. In consequence of the signal national deliverance which divine providence gave them from the infamous machinations of Haman, Mordecai ordered the Jews to commemorate that event by an anniversary festival, which was to last for two days, in accordance with the two days' war of defense they had to maintain. There was a slight difference in the time of this festival; for the Jews in the provinces, having defended themselves against their enemies on the thirteenth, devoted the fourteenth to festivity; whereas their brethren in Shushan, having extended that work over two days, did not observe their thanksgiving feast till the fifteenth. But this was remedied by authority, which fixed the fourteenth and fifteenth of Adar. It became a season of sunny memories to the universal body of the Jews; and, by the letters of Mordecai, dispersed through all parts of the Persian empire, it was established as an annual feast, the celebration of which is kept up still. On both days of the feast, the modern Jews read over the Megillah or Book of Esther in their synagogues. The copy read must not be printed, but written on vellum in the form of a roll; and the names of the ten sons of Haman are written on it a peculiar manner, being ranged, they say, like so many bodies on a gibbet. The reader must pronounce all these names in one breath. Whenever Haman's name is pronounced, they make a terrible noise in the synagogue. Some drum with their feet on the floor, and the boys have mallets with which they knock and make a noise. They prepare themselves for their carnival by a previous fast, which should continue three days, in imitation of Esther's; but they have mostly reduced it to one day [JENNINGS, Jewish Antiquities].

Wherefore they called these days Purim after the name Pur. This first על־כּן refers to what precedes and states the reason, resulting from what has just been mentioned, why this festival received the name of Purim. With the second על־כּן begins a new sentence which reaches to Esther 9:28, and explains how it happened that these feast-days became a general observance with all Jews; namely, that because of all the words of this letter (of Mordochai, Esther 9:20), and of what they had seen concerning the matter (על־כּכה, concerning so and so), and what had come upon them (therefore for two reasons: (1) because of the written injunction of Mordochai; and (2) because they had themselves experienced this event), the Jews established, and took upon themselves, their descendants, and all who should join themselves unto them (proselytes), so that it should not fail (i.e., inviolably), to keep (to celebrate) these two days according to the writing concerning them and the time appointed thereby year by year.

Pur - This Persian word signifies a lot, because Haman had by lot determined this time to be the time of the Jews destruction.