Hmm...I've never tried to explain it to people who don't know what Aspergers is before; save my closest family and friends, so haven't attempted to do so with strangers yet.
I hope no one takes any offence to this, but for me, I would probably compare myself to an artificially intelligent being; though perhaps this would only apply to female Aspies?? I don't know
Generally speaking, we are able to process large amounts of information constantly; going so far as to test out every possible outcome in our minds. We reason with logic, and may have trouble fathoming he purpose of jokes or lies; at least while we are still new to the concepts.
We are like sponges; everything around us is a new learning experience, which may cause us to appear rather like children; curious, and innocent. We can adapt to the environment around us by mimicry. Sometimes our first few attempts to do so can appear rather awkward, but with practise, we may appear rather 'human'.
We accept the truth as others provide it to us, and so can't always detect deception, though we can process facts, and apply them on to situations, which balances us out in the end. We care more about these logical facts, then how people feel about them at times, and so can easily upset others, without meaning to.
While we may not always understand emotional experiences we have yet encountered in the past, we do feel deeply, and empathise; yet constantly question and analyse our feelings, and the emotions of others.
We also have to live with the 'stigma' of not being 'normal'. We may occasionally wish to be more 'human', so as not to feel so abnormal.
I don't know how everyone else feels about that explanation, but it feels like the simplest, most correct way to explain myself. I have also felt that I can always relate to AI characters in film, and feel this is why.
If anyone wants some examples of films they may reference, I'd recommend: 'A.I.', 'The Iron Giant', 'The Terminator 2', 'Her', 'Bicentennial Man'.