A mobile phone charger has output current 1000mAh (5V) according to battery...

...requirements if I connect a......? A charger has output current 1000mAh (5V) according to battery requirements of an electronics device

if I connect a charger with output current of a little more than 1000mAh the relevant device behaves normal

My question is if a device needs 1000mAh current, does that mean
it can work at maximum 1000mAh or
it means it should be operated at minimum 1000mAh.

and if we connect it with a charger/adopter of output 2000mAh continuosly, will it harm the device ???