What does it mean to put Christ back in Christmas?

Sometimes I get confused about the outrage against the naming of this holiday.

"You can't call it X-mas!  That's taking Jesus out of it!"
"You can't say just Happy Holidays!  This is a celebration of Jesus!  Say Merry CHRISTmas!"

We christians seem determined to make this holiday our own.  All you pagan liberals can go get your own holiday.  Never mind that we sort've stole it from you in the first place (see pre-christian winter solstice celebrations with yule logs and gift giving). 

Anyways, I think the attempt to have the celebration of christmas be centered mainly around the Christ is usually good-hearted.

But I've wondered often if many of us are even sure what we're saying when we beckon for saying Merry Christmas vs Happy Holidays.  Do we even know who or what Christ is and means?

To rule out a startlingly prevalent road I must say straightaway that no, Christ was not the last name of Jesus.  It does not surprise me, though, that this is all the further people grasp in their understanding of the phrase.

Again, to say Jesus Christ is not to say the full-name of Jesus.  Rather, to say Christ is to state the job title of this Jesus.  Of course, one may use Jesus Christ as a proper name for Jesus and that is totally acceptable, but it probably leads to a misunderstanding of who the Christ was.

He is Jesus that is the Christ.  If we could just write that in everywhere Jesus Christ comes up it would give our understanding of the phrase a great deal more clarity.

Here's a definition from Matthew for Everyone:

Messiah

The Hebrew word means literally ‘anointed one’, hence in theory either a prophet, priest or king. In Greek this translates as Christos; ‘Christ’ in early Christianity was a title, and only gradually became an alternative proper name for Jesus. In practice ‘Messiah’ is mostly restricted to the notion, which took various forms in ancient Judaism, of the coming king who would be David’s true heir, through whom YHWH would rescue Israel from pagan enemies. There was no single template of expectations. Scriptural stories and promises contributed to different ideals and movements, often focused on (a) decisive military defeat of Israel’s enemies and (b) rebuilding or cleansing the Temple. The Dead Sea Scrolls speak of two ‘Messiahs’, one a priest and the other a king. The universal early Christian belief that Jesus was Messiah is only explicable, granted his crucifixion by the Romans (which would have been seen as a clear sign that he was not the Messiah), by their belief that God had raised him from the dead, so vindicating the implicit messianic claims of his earlier ministry.

So who is the Christ (or rather, what is true of the hoped-for one that will be the Christ)?  One who would do two things:

1. Be the true king.

2. Rescue Israel from pagan enemies (Rome in the first century)

Why is this important?  For a reason other than the obvious that to tell others to "put Christ back into Christmas" we should probably first at least know what we're saying?

I'd like to pause here and leave the implication to you.

Having looked a bit at what "Christ" actually means, how does that change the outcry for you?  What does putting the "Christ" back into Christmas actually mean?