What does the verse really mean?
Well, look at the stories of Jacob and Esau. Esau sold his birthright to Jacob for a bowl of stew (an act that I'm sure did not please God). Then later, Jacob basically stole Isaac's blessing from Esau, and Isaac blessed Jacob, saying "May nations serve you, and peoples bow down to you. Be lord over your brothers, and may the sons of your mother bow down to you." As you can imagine, Esau wasn't too happy. He demanded a blessing from Isaac, but all he got was "Your dwelling will be away from the earth's richness, away from the dew of heaven above. You will live by the sword, and you will serve your brother." (Texts taken from Genesis 27).
Yeah, Esau was pretty ticked.
Later, Esau purposefully married a Canaanite woman, and many of his descendants were part of nations such as the Hittites, Hivites, and Canaanites. Not exactly God's best buddies. Jacob, on the other hand, eventually became the father of the twelve tribes of Israel, because God honored Isaac's blessing to Jacob.
Which brings me to the point. In the old Testament, the only way to "win God's approval" (or at least have a chance) was by following his commandments. Otherwise, because He is a Just God, His wrath would be upon you, since Jesus had not yet died for the sins of the world. Esau distanced himself from God's chosen people, Abraham/Isaac/Jacob's descendants, and became a Canaanite instead. It makes sense that God would say "Jacob I loved, and Esau I hated."
One has to remember that love, at least in this instance, is a verb. The greek word is ἠγάπησα, which is also used in the New Testament when Jesus says, "Love one another as I have loved you." We can clearly see how God's loved played out in Jacob's life; he did, after all, become one of the patriarchs of the Tribes of Israel. The reason is because of Jacob's choice
The Greek word here for hate is ἐμίσησα. Now, this is a much less common word, and since I obviously do not know Greek, it was hard to find a good translation that actually explained what "hated" meant. From what I gathered, the gist of it is, "loved less". It is only used to compare one person to another; to say, "I loved x less than y." That is how it's used here. And clearly, looking at the lives of Jacob and Esau, we can see how the wrath of God played out in Esau's life/descendants, and how Jacob was blessed because of Isaac's faith and blessing. Therefore, it is logical to say that God loved (as a verb) Esau less than Jacob. This does not mean that God hated (emotionally, as we think of it) Esau, it means that the wrath of God (fully deserved) played out in Esau's life.
Well, that's as best as I can explain it. This is all purely my thoughts (well, except for the greek, which is from Bible gateway and a couple Greek concordances), so you can probably search and find people who have a much better description of it.
And I've just decided that I'll include a song, somehow, in each post.
Today it's "Create in Me" by Rend Collective.
It has nothing to do with the rest of the post, but it's a great song.