Unlike traditional markets, the markets that trade in bitcoin never close, so the price of a bitcoin relative to fiat currencies (like the U.S. dollar) may change from second to second, 24 hours a day, 7 days a week.
Bitcoin doesn't take holidays off either.
The price of bitcoin is determined by the price that people are willing to trade for it. Supply (bitcoin has a limited supply) and demand (people wanting more bitcoin) affect how much people are willing to pay.
You never have to buy a whole bitcoin, though; you can buy a fraction of a bitcoin, and secure it yourself.