For use in annotating the work of an Italian poet, I wish to explain a reference to An sich and für sich: What would be a brief, straightforward, and yet accurate definition of these concepts in Hegel's philosophy?
Sebastian Gardner compiled a Hegel glosssary which is extremely useful if one is looking for concise definitions as a starter. I doubt that you will find many definitions to match your criteria better than these.
That being said: Easy definitions of Hegel's concepts are kind of a self-contradictory idea, so if there are still some question marks above your head, it may be due to Hegel being Hegel (some years of extensive studies help, he's actually quite on spot as soon as you understand the system).
FOR ITSELF (für sich). Reflective, explicit, self-comprehending, fully developed (Miller often translates für sich as 'explicit'). Contrasts with: in itself, in-and-for-itself.
IN ITSELF (an sich). Merely potential or implicit (Miller often translates an sich as 'implicit'). Something is 'in itself' when it is considered separately from other things, and (in the case of a form of consciousness) when it is unreflective. That is why, for Hegel, the in itself is mere potentiality: actuality requires determination, negation, relations with other things. Note that a thing may be 'in itself for us' (an sich für uns), an expression Hegel uses often: this just means that we are considering it as it is separate from other things. Contrasts with: for itself, and inand-for-itself.
A related concept which should be kept in mind is the synthesis of both of them, the in-and-for-itself:
IN AND FOR ITSELF (an und für sich). Completely developed; both at home with itself, and finding itself in the other. It contrasts with mere being in itself and being for itself. Being in-and-for-itself is the condition of the Absolute, God, Spirit actualised.