A bucket of water is made by using a bucket on a water source such as a fountain, a sink or a well. A bucket is the only vessel that can be filled from a well.
Like other vessels filled with water, a bucket of water has everyday uses such as transforming clay into soft clay. A bucket of water can also be used to fill a watering can.
A bucket of water is also used in quests such as Plague City (to soften the soil outside Edmond's house) and Clock Tower (to cool the black cog).
For ironmen, one of the fastest methods to fill buckets with water is in the Lumbridge cellar. Use the culinaromacer chest in the cellar to bank and the nearby sink to fill the buckets.