I've had a few people ask what the difference is between a Eurogame and an American game. The main difference, I'd say, is that American games rely much more on the luck of the player and dice rolls to win. Take a look at a classic of each. Settlers of Catan and Monopoly. Both utilize dice extensively but in far different ways.
Monopoly relies on dice for random movement on your turn and your turn only. If you don't land on the space you want, you don't get to do anything and no other player gets to act during your turn. You win by driving the other players out of the game.
Setters of Catan also uses dice as a major mechanic, but each time you roll, even though you get to take the majority of actions, everyone has the chance to participate through the chance to receive resource cards as a result of the die roll. You may also particpate in the acting player's turn through trading resource cards with them. Nothing like that happens in Monopoly. In Catan, you win, not by driving the other players out of the game, but by being the first person to accumulate a specific number of victory points.
In Monopoly, the board is fixed, Park Place and Boardwalk are always in the same location, as are the utilities. This means the same strategies work over and over. Acquire the same certain properties and you'll probably win. Since the board changes each game in Catan, the same general strategies work i.e. get wood and clay early on and the other resources later, but the specific ones change from game to game.
This use of a morphing game board and less use of the luck of die rolls as a method of winning are what I view as the major qualities that cause an "Eurogame" to differ from an "American" one.