If you're reading this posting, the odds are that you are quite literally a christ. If your name is Jane, for example, it may well be that you could fairly be called Jane Christ.
Some people think that "Christ" is a second name for Jesus of Nazareth. Doubtless there are people who think Christ was Jesus's family name, sort of the way that Windsor is the British royal family's current official name. You can imagine a child referring to Joseph and Mary as Mr. and Mrs. Christ.
Christ is actually more like a title, however -- probably a better usage would be "Christ Jesus," analogous to "Queen Elizabeth" (the Apostle Paul's writings use that phrasing quite a bit), or perhaps "Jesus the Christ." Just what does that title mean?
The English word "christ" simply means "anointed one." It derives from the Greek christos, corresponding to the Hebrew mashiyach or "messiah," both having the same meaning.
In the Hebrew Bible, mashiyach is used (and christos is used in the Greek translation, the Septuagint) to refer to people designated by God for some task or purpose, such as priests, kings (such as David and Saul), and even the Persian king Cyrus the Great. See this article for a more detailed discussion, with scriptural citations; another list of such citations is here and a list of quotations is here. [UPDATE: See here for a Jewish perspective.]
In the New Testament (specifically, in the surviving Greek-language manuscript copies), Jesus is sometimes referred to as ho christos, the christ. Many first-century Jews believed that a divinely-anointed leader -- THE Christ, or THE Messiah -- would someday come to rescue Israel from oppression. See here for quotations. By analogy, when someone in the United States refers to the president, chances are that they're referring to THE president, the one who lives in the White House, as opposed to, say, the president of the local garden club.
How is it that you might be a christ? If you're a Christian, when you were baptized you may well have been anointed with a special oil called chrism, the name of which derives from the same Greek root as christos. See, for example, the Book of Common Prayer of the Episcopal Church, at page 307. If you were so anointed, then you are literally an anointed one, i.e., a christ.
In a less literal sense, all baptized persons, anointed or not, are christs -- they have been set apart for the special role defined by the baptismal covenant (BCP p. 304) and in the confirmation rite in which that covenant is reaffirmed (BCP p. 413). This suggests that the term Christ could fairly be used as an honorific for any baptized Christian. You've probably heard of priests being referred to as Father Bill or Bishop Ben -- imagine the laity being addressed as Christ George or Christ Julie!