Samantha owns a sweater, and Kathrine owns a purse. Samantha prefers Kathrine's purse over her sweater, and Kathrine prefers Samantha's sweater, so they trade. Now Samantha owns the purse, and Kathrine owns the sweater.
This simple example demonstrates value creation at the most basic level.
To put this another way, at the time of the trade Samantha values Kathrine's purse more than her sweater. When they trade, she has received something of greater value to her, so she has created value for herself. But if you look at the other side of the trade, Kathrine values Samantha's sweater more than her purse, so she has also created value for herself through the trade.
This is the heart of the economic process: exchange for mutual benefit. Every economic exchange creates mutual benefit - it creates value on both sides of the transaction.
This basic fact of economics has the strength of a law of nature. It is by true by definition. Value is created on both sides of an economic exchange. If value is not created on both sides of an exchange, it is not an economic exchange in the true sense.
UPDATE July 23, 2010: Just for clarity sake I'll add here that an economic exchange is just one subset of economic activity. There are perfectly essential economic actions in which value is not created on both sides (eg gifts).