The "int" tells the compiler of what 'type' a variable is. "int" stands for integer. In case of the microcontroller used here, "int" also implies that the storage capacity of a variable declared as "int" is 2 bytes (or 16bit). It also tells you that the number stored is 'signed', otherwise it would be "unsigned int...".
Before I tell you too many wrong things, have a look at: "http://arduino.cc/en/Reference/HomePage" and "Data Types".
The whole purpose of variables ( such as "int name = 10;" ) is to use them by name, to manipulate them later. If you just write "10" everywhere, you loose flexibility as the running program cannot change that later.