(Of dead heroes, that is.)
My guess, based on my own gut inclination, has to do with Freyja's glamour, which clouds my senses, and makes me want to wait for Ragnarök in her most pleasant company, even though Odin probably has better stories. Thus, she has her pick of the litter, and those she rejects go with dad.
We had this question in a slightly different form a while ago, and I'm going to give the same answer I did then - that it goes back to the Aesir - Vanir war and the settlement between the two sides. One deity from each side gets half the dead.
This is speculation, and I'm going to go further and say that Freyja goes first because of her particular power. Ursula Dronke suggested, in her book on the poems of the Poetic Edda, that the reason neither side won that war is that Odin's power to kill and Freyja's power to renew life meant a permanent standoff.
(Dronke's book is available from Scribd, by the way, if you want to check it out.)
Since Freyja can bring the dead back (see Sorla thattr for an example of her using this power) I figure she gets first pick of the dead. This would tie in with her being a death goddess, or a goddess of the gates of life and death.
The sources does not say.
While verse 14 in Grimnismál - in which we are told that Freyja chooses half the slain every day and the rest goes to Odin - is not the only place that puts Freya in the role of a death goddess, it is an aspect of her that is not elaborated much on. There is a passage in Egill's saga where his daughter Þorgerðr says that she will soon die and go to Freya, and Snorri, in chapter 20 in Skáldskaparmál, also calls her "possesor of the slain". The name of her hall, Sessrumne, meaning "many seats", and its location next to the field Folkvang, "battle meadow", also fits with this.
Britt-Mari Näsström has suggested two things in connection with this: the first is that Freya and Odin might have a division of the fallen due to some earlier division in initiation rites, and the second is that she here acts as a valkyrie, who also are choosers of the slain. The first is as far as I'm aware mostly speculation since we do not know much about any initiation rites at all, while the second seems more plausible.
But really, there is nothing at all that gives a good indication of why she chooses first, or what criteria she might use.
The first paragraph is based on Britt-Mari Näsström, Nordiska gudinnor, which also contains more material on Freyja as a war and death goddess. The second is based on Freyja – The Trivalent Goddess, also by Näsström; unfortunately, the most interesting page is not available in preview (I found it through Wikipedia, and was able to confirm the above by searching for "valkyrie").
