A simple explanation of mining IMO would be to compare it with rolling a dice.
Imagine if you wanted to get a number that is smaller than 3. You roll the dice and you have a chance of getting 2 and win on your first try but if you get something bigger like 5 you have to roll again. You do this random work of rolling the dice until you get a number that is smaller than or equal to your target.
That's mining. The only "math" in it is the integer comparison.
This is a good explanation.
To explain to someone who doesn't have basic knowledge of bitcoin:
equations have inputs and outputs. For example the equation y = 2x + 4 has one input,
x, and out output,
y. When you pass the input "3" into this equation, the output will be 10 because 2(3) equals 6 and 6 plus 4 equals 10. (remember
PEMDAS).
In order to find a valid block, a miner will need to figure out the input to an equation that has an output below a certain value. The equation that is used is much more complex than my above example, sha256. The equation used is also non-linear, which means if the inputs, 1, 2 and 3 were passed through the equation the output for the input 1 may or may not be greater than the output for the input of 2, and the output for the input of 3 may or may not be greater than the output of 2.
It is very easy to calculate the output based on the input, but it is impossible to calculate the input based on the output. So miners basically use the "guess and check" method by checking many inputs to see what the output is. Unlike most math tests you took in school, there are an unlimited number of possible inputs that can possibly be used to calculate the output.