Hullo there, Pastor.
Mens sibi conscia recti
Mens is as you so correctly state mind, or a mind.
Conscia is the feminine form of conscius which means privy to, in the know with regard to, conscious of.
So together this means "a mind conscious of". But of what? Recti comes from the latin rectum a neuter second declension noun meaning "right, virtue" or more generally that which is right. Here it's in the genitive case. So "a mind conscious of the right thing"
Sibi generally means "for or to (the subject of the sentence)". So we get "a mind conscious of the right thing for itself". I imagine the basic thrust of the dictum is "a mind that is aware of what it is morally right for it to do".
Whiteoctave will be along in a minute. He'll provide a much more learned answer for you.....