It turns out that I belong to the R2 (M124) Y chromosome haplogroup. Now, I'm no molecular biologist but will take a crack at explaining what R2 is. First, as a male, I inherited a Y chromosome from my dad and an X chromosome from my mom. The Genographic project only tests Y chromosomes in men, so the rest of the info below is restricted to Y chromosomes.
R2 (M124) is a Y chromosome haplogroup. A haplogroup is distinguished by a series of alleles at specific locations on the chromosome. An allele is a particular sequence of a DNA coding (GATC for example) at a certain location. [Here, GATC stands for Guanine-Adenine-Thymine-Cytosine each of which is a chemical compound made up of nitrogen, hydrogen and oxygen atoms.] What this boils down to is that molecular biologists look for specific patterns of alleles. In order to classify people into haplogroups, they look for Short Tandem Repeats (STRs) which are repeating segments that have a high mutation rate. [For example, I have a repeat of TAGA 12 times at a particular location which is considered significant for classification purposes.]
To cut a long story short, after examining the Y chromosome for significant repeating patterns, the chromosome is classified into a haplogroup. My haplogroup is R2 (M124) which basically means that my chromosome is the result of a specific set of mutations - M168 -> M89 -> M9 -> M45 -> M207 -> M124 of an African ancestor who was born about 60000 years ago.
For more information, please check out National Geographic's Genographic project, ysearch and the DNA forum. And for more information on R2, please see Jean-Gregoire Manoukian's paper.