Is it a new payment merchant like PayPal?
PayPal is a company, Bitcoin isn't.
PayPal deals with existing currencies like US dollars, Bitcoin doesn't.
PayPal holds your balance for you, can freeze your account, and can stop you sending your money to people it doesn't like. With Bitcoin nobody can freeze your account or tell you how to spend your bitcoins.
Is it a virtual currency like LindenDollars that can't be really used as money? (put money In, but not Out)
Whether it is a currency or not isn't clear, but it is virtual. Some say it's more like a commodity than a currency. It acts a lot like gold, in that there is a finite supply of it, it's valued by some people, and it can be used as money anywhere that accepts it. Also it can be bought and sold for US dollars and many other currencies. At the time of writing 1 bitcoin is worth 4.70 USD, and there are plenty of people willing to buy them from you at just under that price, or sell them to you at just over that price. The price is decided by the market; it trades at whatever price people think it is currently worth.
Is it a new currency system, where people exchange bitcoin addresses instead of real money?
It acts a lot like a currency, and can be used to trade with anyone who accepts it. It is very cheap to transfer between any two points in the world, and very fast compared to transferring US dollars or other currencies.
See this introductory video for a slicker introduction.