Gerber files are a set of files, produced using you PCB Cad software (in your case Eagle).
Typically you produce one gerber file for each layer in the process, For a double sided pcb, these would typically be: copper top and bottom, silkscreen top and bottom, solder stop mask (the "green" color) top and bottom and a drill file, in all seven files.
One process layer can consist of one or more "layers" in your pcb cad software (Eagle), so its important to combine the right layers in Eagle when exporting to one of the gerber files.
If SMD's are involved, it is also common to produce a (set) of SMD Pad gerber file.
If more processes are involved in producing you particular PCB more, each process is likely to have ts own gerber file(s).
Once you have created a gerber file, it can be viewed using a gerber viewer. It is quite adviceable to use this gerber viewer process, to see if the different layers line up correctly. As some times you need to reverse the output, in order to fit the process/tool for that process.
Gerber files have several "standard" formats. Make sure you export to the right gerber format for your particular pcb production house.
Making PCBs can be a lot of fun, but my advice is to make a small test board first, using some of the cheap standard 5x5cm production runs at seeedstudio, itead studio or the like.
/MrAlvin