What is the purpose of the resolution of a digital multimeter
Resolution is how well a meter measures. By knowing the resolution of a meter, you can tell if you can see small changes in the signal being measured. For example, if a digital multi-meter has a resolution of 1mV over a 4V range, then you can see small changes of 1mV (1/1000 of a volt) when measuring a 1V signal.
If you were measuring a length of less than 1/4 inch (or 1 mm), you certainly wouldn't use a ruler with the smallest unit of inches (or centimetres). If the temperature is 98.6°F, it's useless to measure it with a thermometer that only has integer markings. You need a thermometer with a resolution of 0.1°F.
The digits and words are used to describe the resolution of the meter. Digital multi-meters are categorised by the number of bits and words they can display.
A 3½-digit meter can display three full numeric digits from 0 to 9, and one half-digit (only 1 or no display). A 3½-digit meter can achieve a resolution of 1999 words. A 4½-digit digital table can achieve a resolution of 19,999 words.
Describing the resolution of a digital table in words is better than describing it in bits, and the resolution of a 3½-bit digital table has been increased to 3200 or 4000 words.
A 3200-word digital table provides better resolution for some measurements. For example, with a 1999-word meter, you cannot display to 0.1 V when measuring voltages greater than 200 V. A 3200-word digital meter can still display to 0.1 V when measuring voltages of 320 V. When the measured voltage is higher than 320 V and you want to achieve a resolution of 0.1 V, you have to use the more expensive 20,000-word digital meter.