You'll have to have a bit knowledge of what mods spawns on what items to have a chance of directly knowing what the a random combination of numbers mean. If someone is offering you a 3/17/19 for example, they assume you know that that is a small charm with +3 max damage, 17 attack rating and 19 life. A 40/15 would be a 40%ed/15%ias jewel etc ... Most items that get such a combination of numbers are expensive and therefore oftenly traded. Less expensive things will not be recognized by just numbers, but might get a small nickname, and then followed by it's stats in numbers. A good example is the vampire gaze previously mentioned.
In the case of that jewel, you will also find that items with such jewels socketed into them also get number ids, 120/45 helm is a helm with 3 of those 40/15.