Consider the following two balances:
You want to weigh 1 gram of a drug.
If you go to the lorry balance and place a spatula full of drug on the balance, the reading would probably be zero. However, the accuracy of the balance is 1 kilogram which means that the most you can say about the amount of drug on the balance is that it weighs 0±1 kg: you have somewhere between no and 1 kilogram of drug. This would not be too helpful to know.
However, if you used the other balance and you had a measurement of 1.000 g, you would know that the amount of drug present was 1.00±0.01 g ie 1.01 to 0.99 g. This would be a lot more useful to know.
It is important that you choose the instrument with the appropriate sensitivity!
Accurate to 1 kilogram
A balance that is accurate to 1 kilogram means that something that actually weighs 10 kilograms would give a measurement in the range 10 ± 1 kilograms ie in the range 9 kilograms to 11 kilograms.
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Accurate to 10 milligrams
A balance that is accurate to 10 milligrams means that something that actually weighs 100 milligrams would give a measurement in the range 100 ± 10 milligrams ie 90 milligrams to 110 milligrams.
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