It simply means that Christ is uniquely special to God and has his authority.
To sit at the right hand of an earthly king was a place of honor, denoting special trust, authority from, and relationship with the king. It was something that was understood without needing explanation at the time.
If you were to sit at the right hand of the King meant that you acted with his authority. Those who came to you would treat you with respect and obedience, as if you were the king yourself.
It's one of the many demonstrations in the Bible, which is not readily understood by us in our time that made perfect sense to the culture as it was then.
There's an article that explains it a bit differently, with more detail here: http://www.letusreason.org/onenes10.htm
This is an excerpt:
To sit at ones right hand means a place of authority, it was a place
of honor it meant dignity and rulership. Throughout the O.T there are
used what are called anthropomorphism to describe God in some function
or characteristic. this is figurative language describing a certain
characteristic of God it is describing his divine actions from a human
The term at the right hand of God points to his exalted position he
now is active on. There are numerous things that need to be considered
to understand this phrase. The phrase right hand is a metaphor, God
exercises his authority by his right hand.
Right after Peter writes of the resurrection he says 1 Pt.3:22 Who has
gone into heaven and is at the right hand of God, angels and
authorities and powers having made subject to him". If he is God the
Father then they are already subjected to him, If he is only a man,
then the ruling of the universe is in a humans hands. So it is as in
Mt.28:18 all authority was given to him in both heaven and earth. This
is something he did not have as he came to earth in a state of
There are several other ways of stating the same basic thing here: http://biblemeanings.info/Words/Body/Right_hand.htm