Let's talk interest rates on your junk bonds.
Even after all that the US has been through (and is still going through), the United States dollar is widely regarded as one of the safest safe havens for your money. As such it serves as a de facto baseline against which all other investments can be measured, the bar everyone has to pass: if you could earn 4% on a 5-year US Treasury bond, or earn 4% on anything else over the next 5 years, you pick the Treasury bond. In many ways this means that the interest rate on a Treasury bond is the closest single measure we have to the price of money all by itself. If someone is loaning you money, they could be loaning it to the Treasury instead; they are losing out by making this loan to you, and must charge you at least this rate just to break even.
But most people/governments/countries aren't as credit-worthy as the US Treasury. A few are (the US treasury isn't magical, after all, just really good at what it does), but generally they are not. There is a possibility when loaning money to these entities that you will not get your money back. That is risk. All entities have some risk (even the US treasury!), and some have more than others; "junk bonds" have a somewhat elevated level of this risk.
Now, you don't just take a risk on for free (unless you're being charitable or something, but I hope you can find better beneficiaries of charity than the average junk bond). You need to be compensated for that risk. Lenders will demand compensation commensurate with that risk - or they will just walk away without making any loans or buying any bonds because it's not worth it. The difference between the interest rate on a US Treasury bond and the interest rate on another bond, such as a junk bond, is the risk premium - the cost of carrying that risk.
Therefore you can see that the interest rate on a junk bond is the price of money plus the risk premium.
Now, the Federal Reserve adjusts the price of money from time to time, by buying and selling US Treasury bonds until the price is something they like. This means that one component of interest rate on a junk bond is the interest rate on the US Treasury bond, and it is effectively controlled by the Federal Reserve (through that layer of indirection).
The other component of the interest rate on a junk bond is the risk premium. It's not generally possible to know in advance whether or not some company will actually default. People have to guess, and decide how comfortable they are taking that risk. This means that risk is more expensive (and interest rates are higher) when they think the companies in question are going through some hard times, and risk will also be more expensive when people decide that they can't take as many risks (perhaps they've already lost some money and need to take additional steps to protect the rest).
It's definitely very hard for an individual to decide what the risk on a particular bond is. The good news is that you generally don't have to. There are a bunch of rich jerks, hedge funds, retirement funds, insurance companies, and other investment entities out there who spend all day looking at things like bonds, trying to estimate the risk. Their willingness to exploit minuscule differences between the interest rate on a bond and the real risk means that the average bond on the market will be fairly priced, according to what all those people think. Plenty of them can still be wrong, mind you (cf. mortgage-backed securities) but in the general case the price of any security reflects all the information everyone in the world has on it on average, so if you're wrong you're in good company. When you buy a nice diversified bond fund, you have access to a bunch of bonds at a pretty-standard price.
So that's interest rates for you. But you asked about prices. As it turns out, they're the same thing! - just expressed slightly differently.
One way or another a bond is essentially meant to be a stream of payments worth a certain amount in the end - this is why you'll hear them referred to sometimes as a "fixed-income security". The interest rate is essentially the difference between the price you pay now, and the value you receive later, except expressed as a rate. Technically, you could structure the bonds differently (e.g. does the bond pay little bits of interest as you go along, or just pay one big lump sum in the end?) but you can use Math to convert between these two situations, and figure out how much money is worth which when, so it doesn't really matter.
Anyway. This means that rising interest rates means lower bond prices on bonds you already own (and falling interest rates means higher bond prices). So if the Federal Reserve increases interest rates, the face value of your bond funds will fall. Also, if people think that the companies issuing the bonds are too risky, the face value of those bonds will also fall. (You were probably expecting the latter effect, though.)
Mind you, you will still get the same amount of future money out of them as you would otherwise: that's why they're fixed-income securities. However, a higher interest rate means "I can get more money in the future for less money now", and so people will be willing to pay you less for your bond in the present. This is known as interest rate risk. It is higher on longer term bonds, because those have more time to earn interest.