mAh means milliamp Hour and is a unit that measures (electric) power over time. It is commonly used to measure the energy capacity of a battery. In general, the more mAh and the longer the battery capacity or battery life.
A higher number means that the battery can store more energy, so it has a higher capacity. Of course, this also means longer battery life for a given usage.
This can be used to provide an idea of how long a device will last, given a constant (or average) power draw rate. You can learn about Amp Hour or Ampere Hour.
For instance, a 3000 mAh battery could power a device drawing 100 mA (milliamp) for 30 hours. A device drawing 200 mA would last only 15 hours.
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