Ok, I googled it too!
My understanding is that it is a sort of innate sense of "wrongness". That we understand without being taught, it just
feels wrong.
For example: we know that it is wrong to kill people from a young age, without explictly being told "you must not kill people". And if murder was legalised we would probably still feel that it was wrong.
It is tied in with emotional approval or disapproval of other peoples actions, which are based on our own individual moral code.
I am not quite sure but i think "moral sense" is essentially our conscience.
confusing but most thorough explanation I found is here:
http://science.jrank.org/pages/7887/Moral-Sense.html
for when your brain is less boggled
