One of the main differences between herbivores and carnivores (and the various omnivores that rank in between) is what their digestive system is optimized for.

Herbivores tend to have longer (relative to body length), more complex and less acidic digestive tracts than Carnivores. Their systems tend to make more use of grinding and physically breaking down plant fibers to get at the sugars in the material. Even then, herbivores get surprisingly little nutrition from plants and almost always have to by grazing or eating. About 50% of the food herbivores eat is excreted as waste.

Modern farming techniques solves some of this by providing easier to digest feed to the animals, usually high in protein. The feed is often made up of other animals (one of the sources of issues during the mad cow disease problem a few years ago). Herbivores generally lack the mechanical mouth parts to be effective meat eaters, but will eat animal products more or less just fine if presented in a digestible format (they don't produce all the right enzymes all the time and their stomachs aren't quite as acidic, but in some small amounts it can actually be healthy for the animal). If you've ever worked near or on a farm, you'll know about various herbivorous animals eating non-plant items pretty frequently. This article is a no duh that's common knowledge to any farmer.

Herbivores come in a few types as well, ruminants have complex multi-compartmented stomachs. As with anything complex, they tend to have a wide variety of failure modes when eating as well. The complex flora in their digestive systems often creates gaseous environments that don't often have a good way to escape. A surprisingly common vet procedure is to basically just punch a hole in the side of a ruminant to provide a vent for outgassing.

Carnivores tend to have shorter (relative to body length), less complex and more acidic digestive tracts. Protein simply processes faster than cellulose and can be broken down by acids and a few enzymes. Anybody who's owned a dog or cat can tell you that carnivores eat plants all the time. It doesn't digest well though as they simply lack the mechanisms to digest cellulose and usually it comes out more or less like it went in. True carnivores also tend to not have as much or any gut flora, which aids in breaking down and digesting plant matter.

As with many things in nature, life is a spectrum. Most things fit somewhere on that spectrum, cows are more herbivore, while goats (as goat owners can tell you) are slightly less, while lions are on the other end as pretty much carnivores. Bears, apes, humans, dogs, pigs etc. all fit in various places on this spectrum.

Humans have digestive systems that are basically somewhere between a simple herbivore and a carnivore (a horse and a dog). Humans, like brown and black bears have digestive systems that aren't particularly optimized to process plant or animal products, but are optimized to switch "modes" over a short period of time. A diet of largely plants will turn out systems to become more acidic and we'll start cultivating gut bacteria to aid in digestion. A diet of largely meats and we'll start to switch to a more alkaline intestinal environment. One problem is that our systems never really complete either transition, so we're not particularly efficient or complete either way.

Our mouth parts are more like a carnivore than an herbivore, but evolution has reduced some of the more useful hunter parts, our canines are pretty small at this point. However, our molars are still meant for ripping and not flat for grinding like a herbivore's. Our jaws provide vertical movement like a carnivore, not rotary grinding motions like a herbivore. Our stomach capacity relative to our body size is almost exactly within carnivore parameters and we pass food out of our stomach and into our intestinal tract about as quickly. We have strong stomach acid compared to herbivores and our stomachs provide almost no digestive activity (a tremendous amount of digestion occurs in an herbivore's stomach).

Our intestines are closer to a carnivore's, and our feces are produced and have consistency like a carnivore's. We have developed gallbladders (helpful for breaking down animal proteins) and our pancreas is a major contributor of enzymes needed for digestion (unlike herbivores).

In cases where humans need surgical intervention, a surprising amount of our digestive tract can be removed and we'll survive. Herbivores need much more of their tract relatively to survive. Humans for example can live without a stomach, colon and cecum. Herbivores cannot.

What's actually surprising about humans is how well we can live on diets made up mostly or solely of plant or animal material. There's some nutrients we don't get as well out of one kind of material, and our bodies don't produce some of the nutrients that animals on the extremes of the spectrum make naturally. It's likely we were scavengers and opportunists, eating pretty much whatever we could get our hands on. We've had weapons and meat processing tools in our inventory since before we were homo sapiens a quarter of a million years ago. The oldest unambiguous weapons are throwing spears from the Palaeolithic 300,000 years ago in a cache full of thousands of animal bones. Meat processing tools have been found much older than Homo erectus (up to 2 million years ago). We've been hunting and eating animals as part of our diet long enough for evolutionary forces to have an affect. If our ancestors were ever herbivores, it was long long before then (millions upon millions of years), and indications are that we've moved rapidly towards the carnivorous end of the spectrum (i.e. our mouth parts aren't anything like an herbivores and neither are any of our known ancestors). In fact it's known that meat was a major part of Homo erectus diets, but cooking was unknown to them. This diet was so effective that Homo Erectus lasted for well over a million years.