The Second Order was a cadre of wizards; it consisted of the second most powerful group of wizards. Not much was known about the Second Order except that there were tests to rise to the level necessary. One of the tests was likely a test of pain. Zedd stated in a Wizard's First Rule that Giller was the only one of his students capable of using the Wizard's first Rule against him and so was the only one that was worthy of the rank of Wizard of the Second Order. The remainder of his students were of the Third Order.
Giller had the calling, not the gift. As such he could only become a Wizard of the Second Order. This information was shared with Kahlan and Richard in Wizard's First Rule, just after Richard used the First Rule against Zedd to ascertain that Kahlan had told Zedd what she and Richard had been through.
Second and Third Order wizards, those born without the gift but with the calling, had their natural 'spark' of the gift amplified by one born with the gift so that they could function. (Since this was in addition to what already existed, this was possible for the additive gifted to accomplish.) This is distantly related to the processes that the ancient wizards with both sides of the gift used to augment people, and later to help wizards born with only the additive.