No, there isn't second class.
Some flights are all-coach (also known as Economy). Some are coach and business class. Some have coach and first class. Some have coach, business class, and first class.
The higher you go in that ranking, the wider and more comfortable the seats are, and the better the service is.
For example, in coach there may be three seats on each side of the aisle, the rows of seats are close together (not much leg room) and the seats are covered in cloth and don't have a whole lot of padding.
In first class, there would be two seats on each side of the aisle, the rows are further apart (good leg room) and the seats are comfy and covered in leather.
On a long-distance/international flight, in coach you get your meal in a little plastic tray with plastic utensils, while in first class you get it on a real plate with metal utensils, and a glass of wine to go with it.
The maps on this site give a good representation of the difference between the seating configurations. http://www.seatguru.com/airlines/Aer_Lingus/Aer_Lingus_Airbus_A330-200.php