What is a risk?
A risk is the chance that something (usually something bad) will happen because of something else. For example, if you smoke a packet of cigarettes a day for 30 years, you have a 10 percent risk of dying from lung cancer.[1]
Doctors use numbers from research studies to tell them which treatments are likely to work for you. These numbers also tell them about the risk of side effects. If you're a man and your surgeon says you need your prostate removed, there's a risk you'll have erections problems afterwards. Your surgeon may think the risk is too low to worry about. But you may think any chance is too high. This is why you need to understand what risk means  so you can take part in treatment decisions.
Imagine you're tossing a coin. It has two sides: heads and tails. So you have a 1 in 2 chance that it'll come up heads, and a 1 in 2 chance that it'll come up tails. It's the same chance every time, however many times you flip it. That's a 50 percent chance.
Percent just means 'out of a hundred', so 50 percent looks like this:
Here's a medical example. Imagine your doctor says "There is a 50 percent chance you will be cured by this drug." If 100 people like you were treated, chances are that 50 of them (the red dots above) would not be cured, while 50 (the white dots) would recover. Here are two more examples:
The thing to remember is that, in both cases, the white dots show your chance of being fine.
If you see numbers like 0.8 percent, this means the risk is less than 1 in 100. The more zeros there are after the decimal point, the lower the chances. For example:

0.008 percent risk is 8 in 100,000

0.0008 percent risk is 8 in 1 million.
Those are the basics of the chance that something will happen to you. Don't worry if it seems difficult. Everyone has trouble with it. Just bear in mind that a low chance of something happening does not mean that there is no chance. Remember that that 1 person out of 100 (one of the pink dots in our diagrams), still means one person will have that side effect.
Next section: How do I use risk to choose treatments?