What value does ammeter or voltmeter measures (RMS, Average or Peak )?
RMS measurement, like average and peak, only applies to measuring AC, though it may be superposed to a DC offset.  

Measuring RMS values is a bit more expensive than measuring average values, so most multimeters avoid the former. Instead they presume your signal is a sine and measure the average value for the rectified sine or the peak value, after which they apply a conversion factor to find the presumed RMS value.  


  \$V_{RMS} = 0.71 \times V_{PEAK} = 1.11 \times V_{AVG}\$  


For other waveforms than sines this calculated RMS value will be wrong! The ratio \$\dfrac{V_{PEAK}}{V_{RMS}}\$ is known as the signal's crest factor, 



and this can be significantly larger than the \$\sqrt{2}\$ value for the sine. If the crest factor is 3 and the multimeter would actually measure peak voltage you would have a 100% error for the calculated RMS value. Usually this error is smaller when the averaged rectified signal is measured instead. We're talking about the form factor then instead of the crest factor.
So the lesson is: be very careful when AC measuring anything else than a sine on those multimeters.

Solution: some more expensive multimeters measure "True RMS".



Just like measuring averages true RMS measurement includes an averaging over a certain period. Only when this period is an exact multiple of the signal frequency this will give the most accurate result. If this time constant is a multiple of 100ms accurate results for 50Hz and 60Hz are possible (5 periods and 6 periods, resp.).
Thomas points out that not all True RMS multimeters can measure AC superposed to DC.



Further reading:
AC Voltage Measurement Errors in Digital Multimeters (Agilent application note)