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Hadeeth authenticity vary on different levels.
The three main categories are:
Saheeh (Authentic)
Hasan (Sound)
Da'eef (Weak)
Hadeeth are graded according to their isnaad's or chain's of transmission.
The narrators that head back to a sahabi (companion of prophet Muhammad) are analysed and a verdict is given by a scholar on the authenticiy of a hadeeth based on the analysis of the narrators. The grading of a hadeeth is based on the lowest level of a narrator. So if all the narrators meet the saheeh criterion, the hadeeth is classed as saheeh. If however one of the narrators was to be da'eef then the hadeeth would be classed da'eef.
Saheeh hadeeth are those hadeeth were all the rawi's (narrators) are all noted to have met each other and have heard hadeeth from each other, are known to be pious and of good character, are known to possess a good memory. These hadeeth may be quoted freely as they are all authentic.
Hasan hadeeth are those hadeeth where one or more of the rawi's have a defect in their memory but not one of great significance. These hadeeth may be quoted freely except in matters of creed where there are no saheeh hadeeth to agree with them.
Da'eed hadeeth are those hadeeth where one or more of the rawi's have a significant defect in memory, were mentally ill, were of bad character and piety or were known to mix things about or change meanings. These may not be quoted freely but may be used as back up for a point established by a saheeh or hasan hadeeth.
Besides from these there are other categories such as mawdoo, marfu' etc and other sub categories of the above ie. saheeh li ghayrih, hasan li ghayrih, da'eef jiddan etc.
