First, what does it show?  The plot displays a fair amount of scatter but seems to suggest the existence of a crude linear relationship between the two variables, which is what Kirchner implies by drawing a best-fit linear regression line through the data.  Alternatively, the data may be equally well characterized as a two-dimensional distribution enclosed by the sides of a piece of pie that has its apex anchored at the point defined by the coldest temperature and the lowest CO2 concentration of the data set.  In fact, this characterization may well be preferred, for when the current temperature-CO2 state of the world is plotted, it falls far below the linear relationship derived by Kirchner but right on the lower side of the piece of pie we would place over the data (the upper side of the pie being Kirchner's line).

Second, what does it mean?  Kirchner notes that "despite greenhouse gas concentrations that are unprecedented in recent earth history, global temperatures have not (yet) risen nearly as much as the correlations in the ice core records would indicate that they could."  He points out, for example, that his representation of the ice core data suggests that "for the current composition of the atmosphere, current temperatures are anomalously cool by many degrees."  How many?  Kirchner's temperature vs. CO2 relationship suggests approximately 10°C, which is significantly more than the maximum warming that is currently predicted by the Intergovernmental Panel on Climate Change to accompany a doubling of the air's CO2 content (which prediction is itself believed by most people to lie outside the realm of reality).  Our characterization of the data, on the other hand - although also suggesting that current temperatures are a bit on the cool side (of the piece of CO2-temperature pie we have baked) - indicate that earth's current temperature is not "anomalous."

Kirchner's second graph, a plot of temperature vs. atmospheric methane concentration, is also of great interest.  In this case, the relationship described by the data is absolutely and unquestionably linear, i.e., there is no room for any pie at all, and it exhibits very little scatter.  However, when it is used to compute what the temperature of today's earth "should be," on the basis of its current atmospheric methane concentration, the result is fully 40°C more than the planet's current temperature; and there is probably no one who would consider that result to be realistic.  Hence, this graph too provides no basis for characterizing earth's current temperature as anomalous.  Rather, in both the case of methane and CO2, it is the atmospheric greenhouse gas concentration that is anomalous.

What is the take-home message of these observations?  Since Kirchner's temperature vs. atmospheric methane concentration plot reveals such a tight coupling of temperature and methane - but the relationship between the two parameters is such that methane cannot possibly be the determinant of temperature - we conclude that temperature must be the determinant of atmospheric methane concentration, as long as humanity is not a part of the picture.  For nearly all of the past 400,000 years, this latter restriction has applied. As our numbers and impact on the biosphere have skyrocketed over the past few centuries, however, we have clearly outgrown this relationship, causing the atmosphere's methane concentration to rise to levels that are far above anything experienced throughout the entire history of the Vostok ice core.  Further supporting our view of what causes what (in the absence of anthropogenic influences) is the fact that earth's temperature has clearly not responded to the anthropogenic-induced methane increase.  In fact, earth is currently about 3°C cooler than it was during the peak warmth of the prior four hundred thousand years, when the air's methane concentration was only 40% of what it is today.

By analogy, we conclude pretty much the same thing about temperature and atmospheric CO2 concentration, i.e., that it is temperature change that elicits changes in the air's CO2 content and not vice versa, although the scatter in Kirchner's temperature vs. atmospheric CO2 concentration plot is sufficient to allow for significant independent movement by both of these parameters.  And again, our primary conclusion, i.e., that atmospheric CO2 concentration is not a major determinant of earth's temperature, is supported by the same fact referenced in the prior paragraph: the fact that the earth is currently 3°C cooler than it was during the peak warmth of the prior four interglacials, when the air's CO2 content was only about 75% of what it is today.

Consider these two observations together.  Since the time of occurrence of the peak temperature of the past 400,000 years, the concentrations of the two most powerful greenhouse gases in the atmosphere (outside of water vapor) - CO2 and methane - have increased by approximately a third and 2.5-fold, respectively; yet earth's temperature has actually dropped ... and by a full 3°C!  Clearly, the only thing we have to fear about CO2- and methane-induced global warming is fear itself, plus the climate alarmists and politicians who are trying to convince the world that black is white, and white black, and who are succeeding very nicely in that endeavor.

Reference
Kirchner, J.W.  2002.  The Gaia Hypothesis: fact, theory, and wishful thinking.  Climatic Change 52: 391-408.