Scaling Voltage for Arduino Analog In, Beyond Voltage Dividers
Signal conditioning in this sense is extremely common. You want to use an amplifier in order to make that 10mV range span (for example) the entire 0-5V range of the arduino. This can be done using op-amps such as the LM741. You'll proabably also want to use a "voltage clamp" (ex: two zener diodes) on the output of your signal conditioner/input into the ADC to make sure that the value does not exceed 5V. If you look around online at op-amp data sheets and/or signal conditioning circuits, you should find guides as to exactly what you are looking for.