Buckets are items that are used for Cooking. You can Craft them with logs, purchase them in Shops or find them on the floor in Everbrook. Water bucket is used for making Bread and Milk bucket is for Baking a Cake.
You fill a Water bucket from the wells scattered throughout Everbrook, or by standing under the waterfall in Jafa after completing the Desert Bundle or it can be purchased from the Spear Salesman in Jafa after completing the Desert Temple Quest.
You get a Milk Bucket from killing a Cow with a bucket in your inventory.