Low glycemic dieting is usually associated with the South Beach Diet instead of Atkins, but they're almost the same thing. It's basically all about how a given food affects the blood sugar level. The higher the glycemic rating, the faster your blood sugar spikes.
Some foods with a low and/or acceptable glycemic rating:
Almonds, Cashews, Walnuts
Cheese in general
Animal protein - fish, steak, eggs, etc.
Green veggies, such as broccoli, asparagas, etc.
The South Beach Diet allows you to eat certain items that are considered to be at a higher glycemic content, as long as you abide by certain rules - such as "Apples must be eaten with skins", which slows down absorbtion of sugars,etc.
Bad stuff - obviously, cane sugar, but also anything with simple sugars, such as starchy foods like pasta and bagels. You can eat a limited amount of pasta on the diet... but it has to be limited and you have to eat protein before eating the pasta. (This slows down the break-down of the starch in the pasta, keeping the blood sugar more stable.)
Atkins moderates the blood sugar spiking by eliminating "carbs" - which are starches, sugars, etc. Like I said, they're close....