The chances are you have associated noise with your signal which is why an oscilloscope can be of help as you can see the noise.
Assuming you have a 10mV signal with 1mV of noise. Your DVM will easily pick up the noise and try to average it, but with the random nature of noise it will not give a steady reading.
On a larger signal of say 1V, the DVM will be on a higher range so the 1mV noise will be insignificant and possibly be below the least significant bit of the of the analog to digital convertor in the DVM so won't show up. Even if it can be measured, it maybe below the resolution of the display. i.e its measuring it but cannot display it.
Measuring low level signals will always be a problem without a proper measuring environment as mains hum (50/60Hz depending where you are) can get everywhere. Especially onto multimeter leads. Strip ceiling lights, energy saving lamps and CRT TV's are terrible radiators of mush.
You could try twisting the measuring leads together to increase the common mode rejection of interference. i.e. a meter measures the difference between its inputs. By twisting together, you reduce mains born (and other external noise from motors) as this noise is induced in both leads at the same time and the meter can reject this to a certain level.
The technical term for this is Signal to Noise Ratio. The higher the better.
As previously mentioned, an analog meter won't physically respond to such changes unless the are large spikes. The kind caused by motors (fridges) coming on and off.