Paleo Diet comes at health and weight loss from the theory that evolution is a long, slow process, and our bodies are still designed for a hunter / gatherer diet.
Before we domesticated plants and animals for food, we had to hunt it down. Meats had a very low fat content, and the fats available were mostly of the Omega-3 fatty acids in fish, and mono polyunsaturated fats; known as the 'good fats'. Fruits, vegetables, and nuts in season would have been the primary sources of nutrition. There would be very little to no grains and legumes (including beans), as well as no form of dairy- these coming after we started becoming agrarian.
So, how and why would this work? First, let's address this as a weight loss issue. In order to lose weight, you must use more calories than you consume. The biggest problem with this, sticking with the evolutionary part of the equation, is that our bodies do not understand a stable food supply, and therefore see all reductions in consumption as a threat, and will do all it can to alleviate the problem. Ask anyone who has been on a diet regimen and they will tell you the hardest part is hungry pangs that feel like you have rough rocks in your stomach. The best nutrition source to remove hunger is protein, and the best source of protein is lean meat. Add all the low-glycemic load fruits and vegetables you want, and your body will not be screaming for more.
Most people notice they feel less drained through the day, which naturally lends itself to increased activity.
There are several questions about the viability of this lifestyle, the most common being: Without dairy, how can you possibly get enough calcium? (Remember, our ancestors did this without supplements.) There is some calcium in meats and lots in various vegetables, but now near the RDA; so why do not we see more evidence of osteoporosis in ancient man? The answer is in digestion. A typical 'western' diet is heavily loaded with foods that have an acid balance; most dairy, cereal grains, salted food, meat and legumes. These take the place of fruits and vegetables, most of which are base and alkaline. To keep the digestive tract functioning properly, there must be something that balances it. The body accomplishes this by taking calcium out of the system. The more you remove, the more you have to replace; therefore, if your diet is running base, you do not need as much calcium to maintain healthy bones.
How do we get fiber without 'whole grains'? Fruits and vegetables (particularly those of the leafy green variety) are not only high in fiber, but much better sources of vitamins and minerals. Additionally, grains contain phytates, which actually retard calcium, zinc, iron, and magnesium absorption.
Other than legumes and grains, are there things that should be avoided? Things that have a high glycemic load should be eaten sparingly, such as tubers. Also treated fruits, by removing the liquid, condense the values and increase their load by weight / volume. Canned items should take the liquid they are packed into into account, but otherwise fresh or fresh frozen are pretty much wide open.
Some of the noted benefits of the paleo diet are a reduction in auto-immune and chronic inflammatory diseases, diabetes, hypothyroidism and insulin resistance.