In single progression, you advance in one variable. For example, if your progression is reps, you might do 3 x 5 x 135 this workout, then aim for 3 x 6 x 135 next workout, and 3 x 7 x 135 on the following one. The sole progression is total reps. A single progression of weight could be 3 x 5 x 135, then 3 x 5 x 140, then 3 x 5 x 145, etc.
In double progression, you advance one variable from the bottom of a range and then change another variable. For example, you might do 3 x 8-12 reps x 135. You start at 3 x 8 x 135, and try to add reps until you reach 3 x 12 x 135. Once there, you bump the weight up to 140 or 145, and then start over again at 3 x 8. You advance the second variable only when you reach the top of your range on the first variable. It only sounds confusing, but it's rather common in practice - you do 3 x 10 x whatever in the gym, and when you can get all 10 reps on all three sets you raise the weight. Then you stick at that weight until you hit your goal reps.