Reads the value from the specified analog pin. The Arduino board
contains a 6 channel (8 channels on the Mini and Nano, 16 on the
Mega), 10-bit analog to digital converter. This means that it will map
input voltages between 0 and 5 volts into integer values between 0 and
1023. This yields a resolution between readings of: 5 volts / 1024 units or, .0049 volts (4.9 mV) per unit.
It is likely what you are seeing is noise and is to be expected. The source of the noise is likely multiple and could be environmental physical metallic or magnetic objects some distance away that are moving, electrical wiring (mains) nearby, and noise introduced by the power supply to the Arduino.
If you want to get a stable precise reading that close to the minimum step size, you will want to take several readings and average them. The more you read and average, the more you can eliminate the random effect of the noise, but the tradeoff is that it is slower because you are taking tens or hundreds of readings just for one result.