Does a weighing scale measure weight or mass? When we stand on a weighing scale the reading we get is in $\mathrm{kg}$. Does it refers to mass or weight?
 A: It measures the force your body exerts on the scale due to gravity. That is, it measures your weight force $F_w = mg$. A low-tech example of this is a spring scale which uses the scale displacement, $x$, due to your weight force and the known spring constant, $k$, to determine your mass via
$kx = mg \implies m = \frac{k}{g} x$
The scale then reads out this mass, $m$.

More technically, the scale measures the normal force acting on you from the scale pushing up on your feet. So, if you are accelerating with respect to the Earth's surface (example: elevator) or, you are under influence of a different acceleration due to gravity, $g\neq g_{E}$, (where $E$ stands for surface of Earth) or a combination of the two, the scale will not read out your mass, but taking the mass readout $m_{scale}$ and multiplying it by $g_E$ will tell you the normal force $F_N$.
So, starting again, in general take a situation where the acceleration due to gravity is $g$ and you are also experiencing an acceleration $a$ (where positive $a$ means acceleration away from the gravitating mass) we have a normal force
$$F_N = m~(g+a)$$
now the scales takes this weight and divides by $g_{E}$ to give its reading, so we have
$$m~(g+a) = m_{scale}~g_E~~\implies~~m_{scale} = \frac{g+a}{g_E} m = \frac{F_N}{g_E}$$
This is the value that the scale will display, which we see, isn't your mass unless $g+a = g_{grav}$.

We see that the answer initially given at the top is the limiting case of $g=g_E$ and $a = 0$, and have now given a more general answer.
I hope this clarifies any problems.
A: I disagree with Will. In all cases I could conceive, the scale directly measures the Normal force acting on you. For example, if you are in an accelerating elevator, the scale would read whatever your calculated normal force is. 
Since I'm currently studying Chemistry, I would like to add that chemists make no distinction between mass and weight. In fact, there is a conversion factor from $\mathrm{kg}$ to $\mathrm{lb}$: $$1\: \mathrm{kg} = 2.2046\: \mathrm{lb}$$
Of course, they never have to deal with cases where the normal force is NOT equal to the gravitational force acting on the object; still, it's incorrect to think of mass and weight (normal force) as interchangeable. It's almost as bad as thinking momentum and velocity are the same thing!
