Apparently I can’t figure out which one is suitable and why?
It[color=red]'s mean that
It mean[color=red]s that
Kindly Explain 
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first is ungrammatical
second is fine
could you expand your sentence so that we can see what meaning it’s trying to convey?
If the first is in something like this:
It’s mean that you are not allowed to go on the trip, but your brother can.
It means:
it is unfair that…
‘mean’ is an adjective.
It means that…
This is the 3rd person singular form of the verb ‘to mean’.
hmm OK
It means that she is right.
It’s mean that she is right.
which one correct?
It means that she is right. (‘it’ shows that she is correct).
It’s mean that she is right
would indicate
It is unfair or unkind that she is correct,
which is not the likely meaning.