A company that sells food products (and certainly more). Blue Sun logos are seen on food cans and advertisements throughout the 'verse. The motto from their commercials: Live life with Blue Sun.
Is that all? Hardly. Joss hinted several times that Blue Sun is more than a food corp -- a sort of ubiquitous Coca Cola-like shadow government.
...and even when it's not. Remember in Shindig when River freaks out while Book and Simon and Jayne are playing cards? What's she doing? Why, she's tearing labels off of the food cans, and she's talking to herself:
RIVER: There it is, there it is. It's always there if you look for it. Everybody sees and nobody sees it...
River has three cans unlabeled, and she's crushing a box of crackers. It has a visible, not emphasized, "Blue Sun" on it. She gets more violent and loud as she continues.
RIVER: These are the ones that take you! Little ones in the corner that you almost don't see. But they're the ones that reach in and do it. They're the ones with teeth and you have to smash them!
RIVER: A million things, and the hands go everywhere and when you brush your teeth all the little blue things are there but no one says it because, because sometimes they're afraid. And then they come...
The hands go everywhere.
Two by two, hands of blue.
Well ain't that something. River obviously knows quite a bit about the Hands Of Blue (HOB) guys -- they're hunting River, and clearly tied to The Academy. It also seems they're connected to Blue Sun, and/or that River does NOT like Blue Sun.
For example, towards the beginning of Ariel, River attacks Jayne with a knife, slashing him across the chest. We're led to believe it's simply because he was giving Simon a bad time and that she has no impulse control.
JAYNE: You owe me a new shirt.
What shirt did she ruin by slashing it across the chest? Well, that would be the one with the Blue Sun logo emblazoned across the chest.
RIVER: He looks better in red.
Also in Ariel, when Simon starts up the Neuro-Imager in the hospital, the image of the Blue Sun logo appears above River as it is starting up. This would indicate a link with medical research.
So who are Blue Sun? How far up the heirarchy are they? Or do they operate outside the heirarchy? In Ariel, the HOB killed an entire station full of Alliance soldiers as though it's standard operating procedure. Are the HOB part of the The Academy? The Alliance? Blue Sun?
Is there a difference?
Blue Sun Serenity sighting: