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When I set my altimeter to 29.92 mm Hg, I have my pressure altitude.
However, what am I doing, when I set my altimeter before each flight. My instructor tells me to hear for AWOS, and set the altimeter accordingly.
Lets say I set it up to 29.77 mm Hg, what is the value I have on my altimeter now?
It is not pressure altitude. My instructor also mentioned the AWOS at the airport, is not corrected for Temperature.
When you are at an airport and you set your altimeter to the setting received from AWOS, ATC, ATIS etc. your altimeter will read your current "true" altitude above mean sea level (msl).
Generally what your altimeter is showing is assumed to be the airport's "airport elevation." The altitude displayed is usually very close to the published airport elevation. However, the "published" airport elevation is actually measured from the highest point on any usable runway, which may not be where you are actually located on the airport at the time you set your altimeter.
At Atlanta (ATL) for example, the published "airport elevation" is 1026 ft. above msl. However, the elevation at the approach end of Runway 27R is 985 ft. above msl, a difference of 41 ft. So, if you have ATL's current altimeter setting set and you are on the approach end of Runway 27R your altimeter should be showing 985 ft., (not 1026 ft.) which would be accurate.
@JohnK provides an excellent answer. But I thought it would be helpful to add some additional information to help you fully understand what is happening when you set the local altimeter setting while on an airport.
When you set the local setting in the Baro window of the altimeter, it should indicate your actual field elevation.
It works the other way around. If you don't have an altimeter setting, you dial the knob on the altimeter until it shows your field elevation. Voila! You're local altimeter setting is displayed in the Baro window.
Temperature corrections are not applied to altimeter indications except when it's below freezing and you are flying an IFR approach, where the errors can cut into obstacle clearance margins depending on how cold and how far above the setting source you are. The colder, and the farther above the setting source, the bigger the error.
The rest of the time, temperature errors from being above or below standard (59F/15C at sea level) are no big deal because they are small and everybody around you has the same error, so it's not worth the trouble to apply a correction for a few feet here or there.
