Incorrect: He is a very unique personality.
Correct: He is a unique personality.
This same logic applies to other words which reflect some kind of absolute: absolute, overwhelmed, straight, opposite, right, dead, entirely, eternal, fatal, final, identical, infinite, mortal, opposite, perfect, immortal, finite, or irrevocable.
In most cases they cannot be modified by very and similar words, nor can they be used in comparisons.
Many times there is a similar word which is not absolute. For example, instead of using the word unique in the above example use a similar word that is not absolute.
Incorrect: He has a more unique personality than Marie.
Correct: He has a more distinctive personality than Marie.