Q:

What is the meaning of output of an accelerometer

I know this question is not fully related to aviation, but I assume the people on this subsection will also have some idea.
Suppose I have an accelerometer resting on a table(flat surface, horizontal). When I look from directly above, I see its reference coordinate system(it is labeled on it) as follows:

(from this site)
When I monitor the accelerometer readings (Ax, Ay, Az) , 
X and Y values are 0 initially(as they should be), and when I push the accelerometer(well, I am pushing the entire breakout board indeed) in the +x direction let's say, there happens an increase first and a decrease when I stop pushing it( I guess because of inertial acceleration ) in the Ax value(in terms of g) which is not surprising. Same for the y axis movements. 
So this makes me conclude that the g in here is pure 9.8 m/s^2 without the sign.
But when it comes to z axis I am getting confused. In the above setup  - in which positive z axis is pointing through the ground - when horizontal and no external force is applied(other than gravitational); Az value is -1, i.e -g or -9.8 m/s^2.
There the question, what does this accelerometer output actually? In such a standing on a surface scenario, there is only a gravitational force on the device and it is pointing towards +z direction. So should not the sensor give + 1g instead of - 1g ?
I guess I have misunderstood some concepts about these sensors(accelerometers).
Please explain me, thanks. 

A:

When the sensor is horizontal (back of the PCB flat on a level table) with the package of the chip "up" (so you can read the printing on the chip) the Z axis should read about +1g and the X and Y should indicate close to zero depending on how close to horizontal the package is. 
The X and Y readings are proportional to the cosine of the angle to level. The Z reading is proportional to the sine of the angle to vertical.
It is not possible to distinguish gravity from acceleration (Equivalence Principle). 
Edit: An acceleration of 1g upward behaves the same as gravity downward. Imagine you're in an closed room floating in space, and then the room is accelerated upward at +9.8m/s^2, the force you feel inside the room would be the same as the gravity on earth. 

