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This is a prediction of the battle of Badr, which was to take place eight or nine years later, in the month of Ramadan, 2 H. (corresponding to January, 624, of the Christian era), when the Muslims decisively defeated a very much superior force of pagan Quraysh (see introductory note to surah {8}). The expression "on that day" has in this context the meaning of "at the same time", for although the battle of Badr began and ended on one day, the victories of Heraclius over the Persians took some years to materialize.
"Whom He will." As explained elsewhere, Allah's Will or Plan is not arbitrary: it is full of the highest wisdom. His Plan is formed in mercy, so as to safeguard the interests of all his creatures, against the selfish aggrandizement of any section of them. And He is able to carry out His Plan in full, and there is no power that can stop or delay His Plan.