First number is base defense. This is the defense the armor has when it is first forged.
Second number is Maximum Upgrade. this is the final defense the armor has when it has been upgraded to its maximum level via Armor Spheres.
Third number is only for low-rank armor, and it is Overforge. When you have a piece of armor at Maximum Upgrade, you can then upgrade it even further by using High-Rank materials (HR31+ online). This further increases the armor's defense to the level of high-rank armors, while still retaining the low-rank skills and slot configuration. This is so that, if you really prefer the low-rank version of a set for the skills and slot layout, you can keep those while still getting decent defense for high-rank quests.
It is almost always a better idea to just make the high-rank version of the armor with those materials, as high-rank armors generally tend to have better skills and more slots.
Armor Sphere upgrades are on a per-set basis. You upgrade an armor in a linear fashion, from level 1 to the maximum (usually level 6). Each upgrade requires an armor sphere and some zenny. Which armor sphere is required depends on the armor, but in general better armors require more rare armor spheres. You will eventually have to use better armor spheres. For example, the first upgrade of Leather armor only requires an Armor Sphere, but later upgrades on that same armor may then require an Armor Sphere+ or Advanced Armor Sphere.
Lagiacrus and Rathalos armor, on the other hand, need an Armor Sphere+ just for the first upgrade, and need Advanced spheres for upgrades 5 and 6.
High-rank armors require high-rank armor spheres, Heavy and Hard.