I'd agree, regarding the ambiguity of what "double-locking" could mean... but in this case, I'm 99.9% sure that "double locking" means what Safety0ff suggested. (The original poster provided a link to a picture of a no-name brass padlock.)

In this case, both the left and the right side of the shackle are secured into the padlock body. (This is in contrast to cheaper padlocks, where only one side of the shackle is locked in.) Depending on the exact details of how it's constructed, this can make it both harder to shim open the padlock and harder cut off the shackle. (It doesn't, however, effect the difficulty of picking open the lock.)
Judging by the keys in the sample image you linked to, it looks like it has a pretty unobstructed keyway and not much variation in pin height: it looks like a good practice lock to get started with, to build up some skills and confidence. (Some of the cheaper padlocks require a
lot of tension: try pushing the shackle in while picking it... you might find it much easier to open when you're first starting.)
Hope that's of some help...