First of all, that is a bad translation (NAB maybe?). Here is Genesis VI from the Douay-Rheims Bible (including commentary on the verses in question):
1 And after that men began to be multiplied upon the earth, and daughters were born to them,
2 The sons of God seeing the daughters of men, that they were fair, took to themselves wives of all which they chose.
3 And God said: My spirit shall not remain in man for ever, because he is flesh, and his days shall be a hundred and twenty years.
4 Now giants were upon the earth in those days. For after the sons of God went in to the daughters of men, and they brought forth children, these are the mighty men of old, men of renown.
5 And God seeing that the wickedness of men was great on the earth, and that all the thought of their heart was bent upon evil at all times,
2 “The sons of God”… The descendants of Seth and Enos are here called sons of God from their religion and piety: whereas the ungodly race of Cain, who by their carnal affections lay grovelling upon the earth, are called the children of men. The unhappy consequence of the former marrying with the latter, ought to be a warning to Christians to be very circumspect in their marriages; and not to suffer themselves to be determined in their choice by their carnal passion, to the prejudice of virtue or religion.
3 “His days shall be”… The meaning is, that man’s days, which before the flood were usually 900 years, should now be reduced to 120 years. Or rather, that God would allow men this term of 120 years, for their repentance and conversion, before he would send the deluge.
4 “Giants”… It is likely the generality of men before the flood were of a gigantic stature in comparison with what men now are. But these here spoken of are called giants, as being not only tall in stature, but violent and savage in their dispositions, and mere monsters of cruelty and lust.
It should read the Sons of God, not the Sons of Heaven. Either way, see commentary on verse two for clarification. Read the rest of the commentary for clarification on the other verses. I agree, when I first read the verses from that translation (I have checked; it is the NAB), I was confused as well. Even more terrible than this translation is the heresy provided in the “commentary” which states that this verse is stolen from ancient mythology! How impious, how evil, and how heretical is such a statement! It is disgusting that this is the “norm” for American Catholics; what a joke. The commentary on those four verses mentions mythology as the source a total of three times. It is quite disgraceful. I would recommend that you get a Douay-Rheims Bible. For more information as to why you should do this (other than the implicit heresy of the NAB translation and the explicit heresy of its footnotes), go to the link below. The link has all the information you would want on the Douay-Rheims, and you can order a very nice copy of it from that website. Also, you might want to get a copy of “Which Bible Should You Read?: A Short Comparison and Commentary on Modern Bible Translations” by Thomas Nelson, published by TAN Books. The information on this small commentary is found at the second link below and can be ordered from the same website. God bless.
marianland.com/bible20.html
marianland.com/tan_which_bible_we_should.html