Esau despised his birthright. In order to understand this, first we need to understand what it means in this context to "despise" and also what the birthright was.
What was a birthright?
An abundance of sources will tell you that in the Ancient Near East context, the birthright goes to the eldest son. All sons receive a "portion" of the inheritance of their father, but the one who receives the birthright receives a double portion. He would also be the "head" of the family.
What did despise (בָּזָה) mean?
Different translations have:
Despise (NIV, ESV, NASB, KJV, HCSB, NET, WEB), contempt (NLT), belittle
(ISV), make little account of (Douay-Rheims)
Strong's defines it as:
despise, disdain, contemptible, think to scorn, vile person
NET Bible Notes say:
So Esau despised his birthright. This clause, which concludes the
episode, is a summary statement which reveals the underlying
significance of Esau’s actions. “To despise” means to treat something
as worthless or with contempt. Esau’s willingness to sell his
birthright was evidence that he considered it to be unimportant.
Bottom line: He considered his birthright to be unimportant.
What was Esau's birthright?
God makes a covenant with Abraham in Genesis 17:
I have made you a father of many nations. I will make you very fruitful; I will make nations of you, and kings will come from you. I will establish my covenant as an everlasting covenant between me and you and your descendants after you for the generations to come, to be your God and the God of your descendants after you. The whole land of Canaan, where you now reside as a foreigner, I will give as an everlasting possession to you and your descendants after you; and I will be their God.
This reiterates and expands on the promises God had already made to Abraham in Genesis 12, 13, and 15. In Genesis 25:11, it says that "after Abraham's death, God blessed Isaac." In the next chapter, God speaks to Isaac:
Stay in this land for a while, and I will be with you and will bless you. For to you and your descendants I will give all these lands and will confirm the oath I swore to your father Abraham. I will make your descendants as numerous as the stars in the sky and will give them all these lands, and through your offspring all nations on earth will be blessed, because Abraham obeyed me and did everything I required of him, keeping my commands, my decrees and my instructions.
These are the blessings that Esau was to inherit, in addition to his father's property. He was to receive the promise of fathering many nations, being a blessing to other nations, and a close relationship with God. But this he despised.
Why did he despise it?
In Hebrews 12 we read:
See that no one is sexually immoral, or is godless like Esau, who for
a single meal sold his inheritance rights as the oldest son.
Afterward, as you know, when he wanted to inherit this blessing, he
was rejected. Even though he sought the blessing with tears, he could
not change what he had done.
Esau is implicitly contrasted with Jesus, who is mentioned at the beginning of the chapter:
For the joy set before him he endured the cross, scorning its shame, and sat down at the right hand of the throne of God.
Jesus endured the hardship of the cross in order to secure blessings for all nations. Esau gave in to his momentary hunger in order to forego his blessing. Ultimately the reason he despised his birthright could be said to be that his god was his stomach. Paul has this to say about such men in Philippians 3:
For, as I have often told you before and now tell you again even with tears, many live as enemies of the cross of Christ. Their destiny is destruction, their god is their stomach, and their glory is in their shame. Their mind is set on earthly things. But our citizenship is in heaven. And we eagerly await a Savior from there, the Lord Jesus Christ, who, by the power that enables him to bring everything under his control, will transform our lowly bodies so that they will be like his glorious body.