To answer that would be difficult. It is a very complex thing, dealing with human emotion, supply and demand, energy costs, and effort. The best way, I think, to explain it would be this:
Bitcoin supplies are ultimately finite. There is a limit to the number of "coins" that can be produced, and that limited supply drives demand. As time goes on, it becomes much much more difficult to generate more coins, until there are eventually none that can be made anymore.
Leaving the technical stuff out, Bitcoin is a commodity. Commodities are things that can be bought and sold on a marketplace. The price rises and falls based on how big the supply of the item is (how many barrels of oil there are, for example) and the demand for that item in the marketplace (how many people/companies/countries WANT barrels of oil.)
On a side note, the nature of Bitcoin protects it from fraud and manipulation. No government or entity can artificially add or subtract from the supply, which helps create peace of mind for investors. Eventually the prices will stabilize. This is Bitcoin's greatest weakness and its greatest strength.
It can not be toyed with by humans, but it can also never scale to become a proper world currency. After all Bitcoins have been mined, it will simply not have a high enough number to be effective on a global scale. The average person (in a hypothetical country that switched to Bitcoin) would be doing transactions of one billionth of a bitcoin for everyday things. As such, other crypto-currencies are poised to overtake Bitcoin in the future. They offer all the same security, with much higher supply limits.
I find it all fascinating.