[robinsons]

in very basic terms...

computers never make errors, and can only follow instructions ('the program').
a function takes an input (eg. a deck of cards) and returns something else (eg. a shuffled deck of cards).
If you have a function to shuffle cards based on no external factors, it will do the same thing every time. Run it 1 million times, every time it will give you the same shuffle as the output.
obviously this is no good. therefore, you need to introduce 'random' factors into the shuffle. This can be gathered in many ways, either by a random number generator (which for the purposes of simplicity just spits out a random number every time you ask it to), and also other data - here's where the user input, event timing and thermal noise come in. These can all be measured in a way that is impossible to predict (if you could predict these 'random' factors, then you could simulate the shuffle yourself - given equal inputs, the shuffle will always return the same result - it's just following instructions after all). However these all add in data that you cannot know or predict (minor thermal changes over a very small period of time, mouse movement of different users, the number from the random number generator, etc).
It is this information that makes the shuffle random.

sorry if this is long and drawn out, I've tried to give a simple overview of why they are needed without getting too technical