Outdoors, you need a crystal clear sky to have steady light, and even then the light is changing as the sun moves across the sky. Thin, practically transparent clouds are usually enough to cause a meter to shift.
The lighting is usually more steady with artificial light. But now, small movements by you may be enough to cause a meter shift. That's because indoor lighting is notoriously uneven (due to falloff), and shifting the camera a tiny bit will shift the framing, which in turn may affect exposure.
Finally, if your light level is too low, the meter may not be accurate. It sounds like you're in manual mode. Is the meter also flashing? If the meter is flashing, that means there isn't enough light to take an accurate reading.
First thing you should do is to get out of manual mode. You only need manual mode for times when the meter doesn't work, such as long exposure or certain types of flash photography. Otherwise, if the meter works then the auto modes are better. Learn to set a minimum shutter speed in Auto ISO for the subject at hand, and learn to use Exposure Compensation to adjust exposure (when needed.) It's an easier and faster way to get what you want.
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