If we adiabatically expand a saturated air parcel, the temperature will decrease but this then produces a supersaturated condition (the temperature has dropped below the dew point). Condensation will then take place; the latent heat released will warm up the parcel ("sensible" heat, the kind that changes temperature if transferred, has been added). This warming partially offsets the loss of temperature due to adiabatic expansion. Because of the conversion of latent heat into sensible heat, the process is not truly adiabatic. However, we don't let the released latent heat escape from the parcel, so the process is close to a truly adiabatic one.

The process is reversible if we keep the condensed droplets inside the parcel. Compressing the parcel raises the temperature and causes the droplets to evaporate, re-absorbing the previously released latent heat (so the gain of temperature through adiabatic compression is partially offset by the cooling effect of the latent heat absorption), and thus the final temperature will be the same what we started with.

The dry adiabatic lapse rate gives us the loss of temperature vs. increase in altitude for an unsaturated air parcel. It is fixed at 10 C/km in the Earth's troposphere by the composition of the air and the strength of the Earth's gravitational field.

The moist adiabatic lapse rate is used to describe the temperature of a moving parcel when it is saturated. It is less than the dry adiabatic lapse rate because the condensation heating offsets some of the temperature loss due to "dry" adiabatic expansion, as seen above. The amount of condensation taking place will determine how much of this offset is produced, and hence result in different values for the moist adiabatic lapse rate: when the air temperature is relatively high, the vapor pressure is relatively high (the air is saturated, and at high temperatures, the saturation vapor pressure, which will be equal to the vapor pressure, is high) and the rate of condensation will be relatively high; therefore, the amount of offset heating is high, and we have small moist adiabatic lapse rates (around 4C/km).

The environmental lapse rate is a whole different thing from the adiabatic rates. The adiabatic lapse rates refer to temperature inside an air parcel that is rising or sinking. The environmental lapse rate comes from the variation of the ambient air temperature with altitude. There is no thermodynamic process controlling the environmental temperature; the sun, the wind, clouds, moisture, etc. will affect the environmental temperature and therefore the environmental lapse rate. An average environmental lapse rate for the troposphere is 6.5C/km (which is suspiciously close to the average moist adiabatic lapse rate for parcels).