The "omnivore's dilemma" is a term coined in 1976 by a research psychologist named Paul Rozin and popularized by Michael Pollan's 2006 bestseller. The dilemma facing the animal that eats everything is figuring out what to eat. Or, to quote the first sentence of The Omnivore's Dilemma, "What should we have for dinner?"1
Rats, reportedly, answer this by taking small nibbles of unfamiliar things and remembering what did and did not taste good or make them sick. Humans answer this largely through culture. What we have for dinner is what our mothers made for dinner out of the available foodstuffs where our family lives.
Put that way, you can see how the dilemma sharpens in a society like ours. The set of foodstuffs available where our family lives is approaching the set of foodstuffs available anywhere in the world. And I don't need to go into ethnic enclaves in the big city to get food that doesn't grow anywhere any of my ancestors have ever lived. I don't even need to go into the ethnic aisle of my supermarket; there's a whole lot more than onions and celery just in the produce section.
Pollan's book touches on some interesting and important questions, and I think it's a better book for not hitting the answers too hard. That may be because he admits he doesn't have many answers, though I suspect part of it is that looking for answers would go beyond his idea of writing "A Natural History of Four Meals," as the subtitle of the book has it. (The four meals: Big Corn (from McDonald's); Big Organic (from Whole Goods); "beyond organic" (from Polyface, "a family owned, multi-generational, pasture-based, beyond organic, local-market farm and informational outreach in Virginia's Shenandoah Valley"); and Pollan's own (from foods the author himself shot, grew, foraged, or begged from friends).)
By way of criticism, I'll just say I found the book of decreasing interest as it went along, probably because of decreasing scope. BigCorn is something that affects us all, even if we aren't "industrial eaters." Organic (both Big and "beyond") is more relevant philosophically than practically. And I think Pollan simply overestimates the fascination of his attempt at a meal where he himself is the complete food chain (not least because of the loopholes he allows himself; it's not exactly My Side of the Mountain, Part II to ask a neighbor for some spare bones from the side of beef they bought so you can make a gravy stock for the wild pig you grill on your Marin County patio).
1. This should not be confused with the "hominahominavore's dilemma": if you eat everything you want, you wind up with the physique of Jackie Gleason.