The EASY EXPLANATION!
The easiest way to describe an algorithm is: any set of very detailed and complex instructions which turn one thing in to another. Algorithms only work to their full capability as long as the instructions given are well written. The end result of the algorithm will be all wrong if it's not written out properly.
The best example of an algorithm is a set of instructions for making an air-fix kit. If all the instructions are followed from start to finish, the plane will be exactly as intended. However, if even one part of the instructions is not followed correctly, the plane will not be complete and it may fall apart. Just like the air-fix plane, if the algorithm (in a computer for example) is not followed correctly then the end result will not be what was intended.
Algorithms play a big part in making sure data is protected. They provide important security when there are communication signals over unsecure platforms, like when communications include the internet or other out side networks.
Encryption algorithms also help secure information that is sensitive, so it is much harder to access than if it wasn't encrypted. Passwords use this technique; it is called Hash Algorithm. Another technique used, is called Key management (click on both links to see a more detailed explanation.)