I'm a physicist who was amused by the argument in the comments of this question about gravity. The correct answer about the affect of the accelerating reference frame of the plane on the apparent gravity depends on how the airliner's speed is measured.
I know very little about practical aviation.
When I'm on a trans-Atlantic flight moving 900 km/hr, with respect to what am I moving? Is that my speed relative to the ground (which is also moving)? relative to the local atmosphere (which could be additionally moving due to wind)? relative to some imaginary, absolute grid hovering above the Earth's surface? relative to the "fixed stars"?
This is probably a duplicate, but I can't seem to find the right search terms...
Speed of a plane is actually measured in a number of different ways, and relative to different things. Here is a summary of the different types:
Indicated Airspeed (IAS). This is the number shown on the instrument that measures airspeed, and isn't really relative to anything.
Rectified Airspeed (RAS) or Calibrated Air Speed (CAS) This is IAS corrected for known errors in the instrument and the measurement system.
True Air Speed This is the speed relative to the air around the aircraft; usually found by correcting the RAS for pressure and some other errors.
Ground Speed This is the speed relative to the ground, or a fixed point on the earth ('imaginary grid). Its the vector addition of the True Airspeed (and direction) plus the wind speed (and direction). In olden days this was estimated from the Airspeed and the wind velocity, or through dead reckoning navigation, but now it is trivially found from GPS or other navigation aids.
Planes use different ones of these for different purposes. Measurements relative to the fixed stars are not generally useful until you are in the realm of space travel.
There are multiple speeds referred to in aviation, some of which are not 'speed' in the traditional sense.
Indicated airspeed (IAS): This is a measure of dynamic pressure and not actual speed, measured using the pitot-static system (i.e. difference of the total and static pressure). It is a function of density and airspeed, not speed alone. Usually, the critical speeds are given in terms of IAS as the aircraft behaves similarly in same IAS.
Calibrated Airpseed (CAS): This is nothing but the Indicated airspeed corrected for instrument and position errors- still not an actual speed.
True airspeed: This gives the speed of the aircraft in relation to the sorrounding airmass. This is the speed used in the flight planning (before taking into account wind, that is) and for measuring aircraft performance. This is the speed with respect to the local atmosphere.
Ground speed: This is the speed of the aircraft with respect to the ground and as such akin to the speed of the car. This cannot be measured without an external instrument and usually, measured with GPS.
As far as air travel is concerned, speeds relative to stars are not used, as there is no need for such complexity.
I will try to add some information to the previous questions, which are correct. My intention is to provide you physical meaning, but previous answers are essentially correct.
When discussing reference frames where the speed is usually provided I will essentially summarize in 2:
Airplane reference (aka body axis): is the ideal reference frame attached to the airplane (not usually considering acceleration, but in practice should be done). The upstream speed is measure here (as the air approaches the airplane in this reference frame) and has been mentioned before as best approximation as "True Airspeed" (the other are measured and calibrated speeds).
Ground reference: is the reference located at the ground, usually located just below the airplane. That's "Ground Speed".
If you would like to know further about reference frames in the airplane, there are more reference frames (or variations of the previous one):
Body reference: just intermediate step to define other systems I am coming back to this one. Is located in the center of gravity, the x axis goes along the fuselage from cockpit to tail, z axis along gravity.
Stability reference: is the body reference rotated along y axis to make the external air speed component in the z direction 0. It is usually used to define angle of attack and compute stability of the trajectory.
Wind reference: is the stability reference rotated along z axis to make the air speed in this reference only in x direction. Formally this is where lift and drag are defined. (Notice that in body reference you are propulsed by aerodynamic force at the vertical tail plane. :)) Also, sideslip is defined as the rotation of axis system.
I have seen some literature defining lift and drag in stability reference.
I have seen in structural context to define another reference frame, x as in body reference and y axis along the wing as in body reference. This system is different to Body reference when turning, and used to compute the load factor.
It is very common to assume that the airplane is quasi-stationary, so no acceleration assumed in the frame except for highly precise calculations (or the load factor).