Earth's surface temperature (TS = 288 K) is warmer than its radiative equilibrium temperature (Te = 255) due to the greenhouse effect.
The low figure is what sunlight alone could heat the Earth to, given Earth's solar constant and albedo. The higher figure at the surface is due to Earth's greenhouse effect. The atmosphere absorbs infrared radiation from the ground (and different layers of the atmosphere absorb it from other layers), and radiates its own IR back to the ground. This "back-radiation" adds to the sunlight absorbed at Earth's surface, so the Earth is warmer than it would be from sunlight alone.
Of course, a lot of global warming deniers say the greenhouse effect doesn't exist. Many give the "lapse rate" argument: the warmer surface is due to the Earth's lapse rate, not to the greenhouse effect.
What is the lapse rate?
The lapse rate, for which the usual symbol is a capital Greek letter Gamma (Γ), is defined as the rate at which temperature declines with altitude. For a dry atmosphere--one with no water vapor--there's a simple equation for it:
For the Earth, g, the gravitational acceleration at the surface, averages 9.80665 meters per second squared (m s-2). cP, the specific heat capacity of dry air at constant pressure, is about 1,004 joules per kelvin per kilogram (J K-1 kg-1). So Γ works out to about 9.77 K per kilometer. But real air contains water vapor, a volatile. It evaporates from the ground and condenses at cloud height. Latent heat transfer therefore decreases the lapse rate, so the actual value ranges from about 4.8 K km-1 near the surface to about 9.8 K km-1 near the tropopause, for an average of 6.5 K km-1.
The average height of IR emission to space--let's call it "h"--is about 5.1 km above the ground. Multiply 6.5 by 5.1 and you get 33 K. Subtract that from 288 and you get 255 K, the Earth's radiative equilibrium temperature. It's not really that simple, since what gets out to space varies with wavelength, so the levels from which IR emits to space also varies with wavelength. But you can treat it as if there were a single emission height and an average wavelength (about 10.6 microns [μ]). So, the deniers say, even if there were no greenhouse gases in the air, the Earth's surface would still be 33 K warmer than Te.
This is wrong. They assume the emission height is fixed, a constant of nature. It is not. If there were no greenhouse gases in the air, the emission height would be at the surface, and Earth's surface temperature would be TS = Te = 255 K. The presence of greenhouse gases raises the emission height, and the more the greenhouse gases, the higher the emission level goes. The average emission height on Venus is 65 km. On Mars it's 1.6 km.
If you take the variation of temperature with height as a straight line (it's not quite, but if you did), then the lapse rate only gives you the slope. You may remember from algebra that a straight line can be expressed as:
where Y is the vertical coordinate, X is the horizontal coordinate, m is the slope, and b is the Y-intercept. For our example, TS = 6.5 h + Te.
But the deniers are assuming that they know h, and they don't. h is not a fixed constant of nature. It varies with the amount of greenhouse gases in the atmosphere. The deniers have no theory of what determines h other than the unthinking assumption that it's a fixed number--a dictate of God, brought down from Mount Sinai engraved on a stone tablet. As usual, they don't know what they're talking about.