The exposure meter will correspond to exposure levels. When using spot meter, this is most evident. Zero is equivalent to middle grey. It represent's 12-18% (depending) of the total light available being reflected from the subject into the lens. It will render near level 128 in an 8-bit image, in practice, it won't be exactly level 128, but that's the idea. So if you have half the amount of light in one scene than another, you will need twice the amount of exposure to render a subject at 18%, i.e. increase time, aperture or sensitivity by one stop.
+1ev represents one full stop more light reflected off the subject than 0ev. So if you expose something that reflects twice as much light as something that reflects 18% of the total light available at ±0ev, it will be appear too dark. To properly expose such a subject, you would need to increase exposure by one stop.
-1ev represents one full stop less light reflected off the subject than ±0ev. So if you expose something that reflects twice as much light as something that reflects 18% of the total light available at 0ev, it will appear too light. To properly expose such a subject, you would need to decrease exposure by one stop.
The vital thing to remember is that ±0ev does NOT mean "correct". It means that the same circumstances were met as when the meter was calibrated.