Well, the best way to understand it is to read the book, but I can understand your curiosity.
I eat low-carb, very similar to Atkins, though probably not as strict. On Atkins, you restrict the amount of carbohydrates you eat. One good rule of thumb is to avoid white things - no sugar, no white flour, no potatoes, no rice, no noodles. The only exception is cauliflower I think.
You also avoid eating a lot of fruit. Eventually you can eat lower carb fruit like berries and some melons in moderation.
Your daily diet should be made up of adequate protein (notice I did not say HIGH protein, just ADEQUATE protein), and lots of lower carb veggies. In addition, fat is not a bad word - you are encouraged to eat healthy sources of fat.
Hope this helps. There's a lot more, so you may want to pick up the book - Dr. Atkins New Diet Revolution.