If something is sophisticated, it's complicated and intricate. The inner workings of a computer are sophisticated. Sophisticated can also refer to having good taste. Either way, sophisticated things are impressive.
Sophisticated systems and objects are complex and tough to understand. High school math is a lot more sophisticated than grammar school math. Driving a car is more sophisticated than riding a bike. People are sophisticated if they have plenty of worldly experience and what is generally regarded as "good taste." Sometimes, that just means they have a lot of money and like things that are fancy. Going to a symphony is considered more sophisticated than going to a rock concert.