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I believe that personality is very important, and each person has his  unique way of showing personality.

 Sanjay is correct.  You need a comma.  I also agree with changing their to his, though there has been much discussion on the forum lately about using they (or not) when referring to the singular. 

The sentence doesn’t really have much meaning, though.  If two people have a shy personality, then they each have their own way of showing their shyness?  Do you really mean to say that having a personality is important? Everyone has a personality.  What is so important about that? 

A similar word is personable.  Perhaps you mean that it is important to be personable, and that each individual has a unique personality.