What does "in the image of God" mean? Genesis 1:26:


  Then God said, “Let us make mankind in our image, in our likeness, so that they may rule over the fish in the sea and the birds in the sky, over the livestock and all the wild animals, and over all the creatures that move along the ground.”


Does this mean humans look like God, complete with hands, feet, and sexual organs?  Or is it referring to something else?
There are differing traditions about this. Only in Eastern Orthodoxy have I run into a very specific definition, where 'Image of God' is treated like a term of art with a specific, well defined meaning. 

Generally speaking, most Christians interpret it to mean that we share in the spiritual reality with the spiritual beings, and traits specific to God (spiritual traits, since God is Spirit) belong to man. Such things then do not belong to other creatures, which may or may not include the angels. What traits these are vary from interpretation to interpretation, but they may include:


Ability to create
Reason
Having a 'spirit'
Being able to have the indwelling of the Holy Spirit


In Eastern Orthodoxy, there is a specific definition that is sometimes offered (though it does not exclude the above.)


Each human is unique, as God is unique (being one!)
Each human is relational, that is, he exists only in relation to others, as God is Trinity in himself and thus even if there is no other, God is 'in relation' via the persons of the Trinity
Each human has free will, as God has free will.