Money is not backed at all by anything physical. The government can print more bills at its discretion. It doesn't need permission, it doesn't need to find any more gold or precious gems or make deals with another country, it simply does it. The gold reserves, the real estate, foreign bonds, none of that is backing the US currency, it is all stuff that the US has purchased with currency which it literally created out of thin air.
So if governments can just arbitrarily make more money, why don't they and become the richest country in the world? Because currency is only valuable to people who will accept it: if the US government printed off enough money to give $1000000 to everyone (and in this digital age they don't even need to print it, just electronically hand it out) in the US all that would happen would be everyone in the US could spend an extra million. But then, because everyone has an extra $1000000 you would get rapid inflation: price is effected by supply and demand, when more people have money, demand goes up and supply lags behind so price skyrockets. Spain tried this, they had an influx of gold, turned it all into coins (because they didn't have computers to store numbers like we do) and for a brief moment everyone enjoyed being rich; then inflation happened and everyone was poorer than they started.
There's also foreign trade: the US dollar has no real value in other countries. If you come to Canada, you need to buy Canadian dollars. Think of the Canadian dollar as just another product, and you need to buy it if you want to travel to Canada. You buy CAD from a foreign exchange broker who works with a Canadian Foreign Exchange broker and they reach an agreement. "I have 100 USD. I will give this to you so that you can buy stuff here in the US in exchange for 100 CAD so that I can do the same in Canada", and just like with any other product, the exchange rate is affected by supply and demand: if more people have more money and want to travel more they will need more foreign currency so the price of that currency will go up. This happens whether you explicitly exchange cash or just use your credit card for foreign transactions: someone somewhere is buying and selling the currency you are using. Germany tried doing this as well, and I think we can safely say it didn't go so well.
It's really easiest if you stop thinking about currency as anything special and realize that currency is just another product. I trade 2 pigs for your cow. I trade 2 pigs for $1000. Exact same thing. The biggest difference is that the scarcity is entirely controlled by the government: while they can create money at will they can also destroy money, and this balance allows the currency to remain more-or-less stable year to year, where the number of pigs, cows, crops, and everything else we might barter with can fluctuate wildly month by month.
And this is where bitcoins come in. They have a value because, like any product, someone wants to buy them. They have a purpose and people are willing to exchange their government issued money for them. The fact that it is called a currency is just confusing you, just think of them as stamps, or bottle caps, or whatever arbitrary item you want, and imagine a world where some people really want these items. I can buy fancy old stamps for hundreds of dollars, I can trade those stamps for other stamps, if I find a fellow collector I can bargain them to accept this old stamp for their XBox. If suddenly a lot of people want that stamp, he might then find someone to trade that stamp for a car. The value of the car hasn't come down, the government issued currency I originally used to buy the stamp is still the same value, I can still walk into a store and buy an XBox for the exact same price as I did before the stamp was suddenly worth a car, it's just that now the stamp itself is worth significantly more.
Replace "stamp" with "bitcoin".
To answer your final question "what is backing bitcoins?", I will say again, bitcoins are backed by the exact same thing as the USD, and the CAD, and every other currency in the modern world: absolutely nothing. They have value because people want them to have value. They have value because they are stable and they are stable because the government makes them so.
To answer the ancillary question "how is the price of bitcoins going up while they're effectively just printing them off?" Simply because the demand is outstripping supply: people want bitcoins faster than they can be mined. Following numbers are used for example purposes only and do not reflect reality: 3 days ago one person wanted bitcoins, 2 days ago two people wanted them, yesterday four people wanted them, today eight people want them, but in that time only 2 new coins were created, and those 8 people are fighting over those two coins. This is why I said the current growth is unsustainable, unless 16 people want bitcoins tomorrow and 32 people the day after, the rate of growth will start to slow and eventually stop. Then supply will start to catch up and the demand will start to come down as will the price.
The most interesting thing about bitcoins as a currency though is that, unlike government backed currencies which are arbitrarily created and destroyed whenever and however much they want, bitcoins can neither be destroyed nor created arbitrarily, they must be mined, and once mined they exist forever. Furthermore, while government currencies have no limit to how much they can create, bitcoins are hard limited by the algorithm: one day we will have generated every single bitcoin, and then there will be no way to get any more.
tl;dr;
If it makes you feel better, think of bitcoins as being nothing more than electronic gold, not a currency. It is mined, bought, sold, and exchanged with government backed currencies.
