What does it mean to say that "chimpanzees share 98% of our DNA"?

The two species we are most closely related to are the Common Chimpanzee, and the Pygmy Chimpanzee, or bonobo.  We shared a common ancestor with the chimps about 5 or so million years ago, and then the chimp side of the family tree subsequently split into the two types of chimps we see today.  Therefore we are, logically, equally closely related to either species.  You have propably read that tests have revealed an astonishingly large amount of genetic overlap, so that somewhere in the region of 98% of our DNA is identical.  Is this true?

Yes, but it depends on what you are counting.  If you count base pairs of nucleotides, this is indeed roughly the figure you end up with.  It's a bit like comparing each character in the following two sentences:

• The sun also ariseth, and the sun goeth down, and hasteth to his place where he arose.
• The sun also rises, and the sun goes down, and hastens to his place where he arose.

(The first one comes from Ecclesiastes (in the Bible), as translated in the early 1600s.  The second one is a more modern translation.)  Now compare each letter with its corresponding one.  The first 10 letters match perfectly, but the 11th letter of the first phrase has been deleted from the second phrase.  There's also a problem with the 16th and 17th letters of the first phrase, and so on.

Depending on how you count, you end up with a letter-by-letter correspondance rate of about 90%.  Similarly, you get about a 98% concordance rate when you compare the position of the DNA letters (A, G, C, T) in humans with those in chimps.

But things start to look a little different if you actually compare whole genes.  Let each word in the above two phrases represent one gene, and now look again at how well they correspond - the figure drops to about 82%.  Since it only takes one different letter within a word (or gene) to alter that word (or gene), the concordance rates are generally much lower.  (In this example, the figure was only a little lower, but this is because each word is only composed of several letters.  In reality, each gene is composed of many hundreds to thousands of nucleotides.)

Another way of putting it is that we may share 98% of our DNA with chimps, but for all we know, this could mean that every single gene is different - each by about 2%.

George C. Williams, the great evolutionary biologist, put it well:

If part of some gene in a human cell reads GTTAGCC and exactly the same sequence of the chemical groups (nucleotides) is found in the same place on the same gene in an ape cell, the two are 100 percent similar for this sample.  So what? A gene is made up of thousands of base pairs, not just a sequence of seven, as in the example shown.  For two genes to really be the same, every one of the thousands of base pairs has to be the same.  If proportions of such exactly similar genes are estimated, it may be found that a quarter to a third of the genes may differ in human and ape cells.  Human cells from two different individuals may well differ in several percent of their genes.