Why was 21 million picked as the number of bitcoins to be created? Why did Satoshi pick 21 million as the number of bitcoins to be created? What is the significance of that number?
Here's a mathematical explanation:

Calculate the number of blocks per 4 year cycle:

6 blocks per hour
* 24 hours per day
* 365 days per year
* 4 years per cycle
= 210,240
~= 210,000


Sum all the block reward sizes:

50 + 25 + 12.5 + 6.25 + 3.125 + ... = 100


Multiply the two:

210,000 * 100 = 21 million.


Economically, because the currency is effectively infinitely divisible, then the precise amount doesn't matter, as long as the limit remains fixed.