I didn't quite believe this either when I read it, but simply possessing certain numbers could get you in trouble with the law. You can just imagine the humiliation in prison when your fellow inmate says "what you in for?"
Its all to do with securing and encrypting data. When your files are encrypted on a computer, they are effectively locked with an extremely long number - the 'public key'. Now, to unlock the data, the computer must use this public key which has originated from this computer together with its own private key. Since public keys are published and available to anyone files and messages are not secure in themselves. However this doesn't mean they can be read by anyone because to read it, you need the private key.
The keys are based on prime numbers, which when multiplied together, equal the locks number. Since the numbers contain thousands of digits, its going to take you a long, long time to find the keys, even if you had China's supercomputer! This is what makes encryption so secure because there are an infinite number of prime numbers available and nearly infinite possibilities for keys.
One stupidly long prime number was in fact the source code to unlock the copyrighted systems on DVD's. Therefore, in the hands of the wrong person, could enable them to duplicate, copy and download the data on a DVD. Due to this it has now been considered a tool to get around a copyright system under the 1998 Digital Rights Act.
Personally I think encryption is completely necessary to keep data private, but many argue that there should be backdoors in place to fight terrorism. This is a tough one and there are strong views for and against. Let me know your thoughts in the comments below.
Be sure to check out the video below by Wendoverproductions as it explains this complicated topic in such a way to make it incredibly easy to understand: