When there's an alternative voltage, why does the voltmeter measures rms value instead of the value at that specific time?
If you are measuring a 10Khz signal, what value would you read ? What value would be useful to you ? It would be constantly changing. What good is a constantly changing value on an LCD display especially if its changing so fast. A 10Khz signal has a period of 100 microseconds, so depending on the number of sample points taken, you are looking values changing much less than 100uS. This all assumes that the meter is even capable of sampling so fast.
A light bulb connected turns on and off at 50Hz to 60Hz depending on your region. Do you see if turn on and off ? You don't because our eyes can't detect that change - our eyes are too slow. 60Hz has a period of 16.67ms. Now imagine its changing less than 100uS.
RMS is a fixed value. Regardless of the constant changing values, the RMS value will be fixed for that particular peak or peak to peak voltage.
If you require to see the signal, then a oscilloscope would be better suited.
See comments for corrections about flicker and detectable flicker frequencies for eyes
I'm assuming that you are asking about an old-fashioned moving-coil meter.
These meters measure AVERAGE value, not RMS. An AC meter is calibrated to read RMS voltage with a sinusoidal waveform.
These meters can indicate the exact voltage at some particular point in time IF the waveform is changing so slowly that the meter needle can follow the waveform. This is possible at frequencies significantly less than 1 Hz.
At higher frequencies, the mechanical inertia of the meter movement acts like a low-pass filter and the needle indicates the average value of the input.
There are a variety of properties which tend to be related to RMS voltage. For example, the amount of heat generated by a resistor which is fed by an AC voltage source will be equal to ...
the average of (voltage times current), which will in turn be equal to...
the average of (voltage squared divided by resistance), which will in turn be equal to...
the square of (square root of the average of (voltage squared)) divided by resistance, i.e.
the square of the RMS voltage, divided by the resistance.
Note that while higher quality meters will actually compute the RMS voltage, lower quality meters will actually measure something else (e.g. the peak voltage or the time-averaged rectified voltage) and multiply it by scaling factor. For example, since the RMS voltage of a sine wave will be proportional to its peak voltage divided by sqrt(2), a meter that measures peak voltage would scale its readings by a factor of about 0.707. Since average rectified voltage is about (2/pi) times peak voltage, a meter that measured average rectified voltage would scale by 1.11. Such measurement techniques will work fine when measuring sinusoidal waveforms, but will yield inaccurate results when measuring anything else.
When measuring AC voltages or currents, the value displayed is calculated ('integrated') over some time, this is not an instantaneous measure (contrary to, for example, an oscilloscope)
The indicated measurement is not always the true RMS value, only instruments made for "true RMS" can measure the RMS value of any waveform, simpler ones gives a correct measurement only for sine waves.
The interest of RMS over peak or average measurements is that it indicates the energy, or power, of the signal.
Normal AC power goes through one full cycle (from 0 volts to maximum positive voltages, back to 0, then to max negative, and finally back to zero) 50 or 60 times a second. A normal meter can't read and display voltages fast enough to follow the instantaneous voltage - and if the meter could, our eyes wouldn't be able to make any sense of the result.
The RMS voltage is the effective voltage of that continuously varying voltage, so it the value that is most often of interest to us.