What, specifically, did Esau lose when he lost the birthright, and what did Jacob gain? What did the birthright represent, and why was it so highly prized by Jacob?
When Esau lost his birthright, he lost a greater ownership of his father's property, as well as the position of leader of the family (thinking of family as a whole tribe of people). Jacob may have prized the birthright out of greed, but it's worth mentioning that God spoke to Rebekah in Genesis 25:22-23 and told her that the younger of her sons would rule over the elder. While it doesn't say that this is the case anywhere in the Bible, If Rebekah had told Jacob of this, perhaps he felt he was doing the will of God. This might also explain why Rebekah helped him in deceiving his father (Genesis 27). Again, this is only speculation on my part. You can read more about the Hebrew birthright here: http://www.bible-history.com/isbe/B/BIRTHRIGHT/
Mainly it appears to be a right to a double share in the inheritance. That is, if a couple had two sons, the first inherited 2/3 of the property and the second inherited 1/3. I've read some discussions that he also had additional responsibilities which made this fair.
Side note: Modern Bible teachers routinely talk about how sneaky and dishonest Jacob was in buying the birthright. But it's interesting to note that the only editorial comment the Bible makes about it is not, "Thus Jacob stole his brother's birthright" or "Thus Jacob tricked his brother out of his birthright", but, "Thus Esau despised his birthright." (Gen 25:34b) Thus the position of the Bible appears to be, not that Jacob , was at fault, but that Esau was an idiot. He was a classic case of immediate gratification, giving up (say) a million dollars several decades in the future in exchange for twenty bucks today.
It's worth mentioning that inheritance included father's blessing. Orthodox professor of theology Lopukhin thinks that those blessings had mystical meaning - the son being blessed becomes continuator of testament between God and Abraham, takes ability to "speak" with God and so on.
Also i like Jakob's blessing of Joseph, it's so poetic.