What nutrients are concentrated in citrus peels (not juice)

There are three (to the best of my knowledge) main factors at work here:

1. Pectin. This is a gelling agent, a bit like gelatin. Fruits such as apples and plums are very high in pectin; citrus fruits are not that high in pectin but citrus peels are incredibly high, so if you're using any of the peel, you're getting tons of great pectin.

   Obviously, the more pectin, the faster and firmer it's going to gel. If the fruit doesn't contain much pectin then you're going to have to cook it down a lot or just add actual pectin (you can buy it in stores).

2. Acidity, as you suspect, makes a big difference. It's not just acidity, it's the relationship of acidity to pectin as above. For more details read The Role of Acid in Jelly Formation. Basically, pectin gels best at a pH of 2.5 (almost exactly the pH of lemon juice) to 4.5 (about the pH of sweet grapes).

   It's best to hit the sweet spot in the middle rather than the extreme ends, so you won't generally be using pure lemon juice, you'll be adding some sugar and other ingredients. Which leads me to the final factor:

3. Sugar. As described in The Role of Sugar in Jelly Formation, sugar precipitates the pectin, basically making the pectin molecules less soluble which mimics the effect of a higher concentration. Therefore, more sugar makes the jelly set faster.

So: Pectin-rich fruits + high acidity + high sugar content = fast setting.

There are actually various other factors that affect the pectin (which is pretty much the only gelling agent at work when working with natural fruit jellies) like salts and even alcohol, but in the vast majority of recipes, it's acidity and sugar that are your primary concerns as well as the actual pectin content of the fruit itself.

Fruit contains lots of water. When you take a piece of fruit at home and press it, you end up with sugars, vitamins and other solids dissolved in water. Let's assume that 100 g of just-pressed juice has X g of water and 100-X g of juice.

A manufacturer who sells juice can do several things.

• pasteurize the juice and sell it as-is. This is 100% juice, not from concentrate, and will often be labelled as "contains pulp" for citrus juices, or "naturally cloudy" for apple juice.
• filter the juice, then pasteurize and sell. This is again 100% juice, not from concentrate, sold as "clear" juice.
• Instead of just pasteurizing the juice, he may boil out Y g of water from the juice somewhere close to where the fruit is grown (Y < X, trying to boil out enough water to get only the solids from the fruit will change the taste too much). This is called concentrate. It gets shipped to the packaging plant, where Y ml of pure water are added back before packaging. This is 100% juice from concentrate. The advantage from the manufacturer: he pays per weight for shipping between the juicing factory (which can be somewhere in the tropics where fruit is cheap) and the packaging plant (which is close to where the customer lives). Not shipping tons of water saves lots of costs, and concentrate is less perishable than non-packaged juice.
• Water costs less than fruit juice. If a manufacturer adds 50 g water to 50 g fruit juice (no matter whether from concentrate or not), this is a 50% fruit juice drink. Most customers expect a fruit juice to be sweet and slightly sour, so the manufacturer adds not just water, but water with sugar and acid in it (mostly citric acid). A 96% juice would be if the manufacturer adds only 4 g of water to 96 g of juice.
• as a final note, 100% juice does not mean that the juice is only from the fruit given in the title. Apple and citrus juice is very cheap, but all other juices are expensive (depending on area, there can be other cheap juices too). So, many manufacturers will sell 100% juice which is in fact blended juice - if the package says "Sour cherry, 100% juice" chances are that it is 25% cherry juice and 75% apple juice. Such combinations are given in fine print in the ingredients list, but AFAIK they are not legally required to list the exact ratio of juices used in a juice blend (this will vary between legislations).