The "officialness" hierarchy goes like this: There are three and only three Core Rules Books - PH, DMG, MM. The PH is the rules source for playing the game, PC races, base class descriptions, etc. If something else anywhere disagrees with the PH on those things - the PH is official. The DMG covers such things as magic item descriptions, special materials construction rules, etc. If another source disagrees with the DMG on those things - the DMG is official. The MM covers monster descriptions, templates, etc. Disagree with the MM on those subjects - the MM wins.
If text and a table entry disagree - the text is official.
If the errata says different on any of the above, the errata is official.
If "The Sage" (Sage Advice column in Dragon magazine) says differently than all the above, the Sage is official. [Though I honestly feel it should be pointed out that the Sage's determinations are nonetheless occasionally questioned as to whether they ought to be FOLLOWED, whether official or not. Those occasions are disagreements as to whether a given ruling was in actuality proper and correct.
All other sources are non-official, optional, variant, etc. Some are effectively authoritative on their subject matter - such as the Expanded Psionics Handbook on the subject of psionic races, classes, abilities - but that doesn't make them "Core" material. Psionics, e.g., is not a "Core" concept; it's optional material.
There is also the SRD but try not to confuse that. It's not the same thing as "official" or "core" material, though it can be taken as authoritative in many discussions. SRD material is not provided for purposes of rules authoritativeness, but for indication of what is freely distributable for publication, etc.