Bucket fields can be very useful to group records in a report. Watch this video until 2:30 and read the examples below:
Example A (Numerical Buckets): I'm viewing a list of all family members associated with my program, and for some reason I need to group them by age. I want to know how many of the clients are less than 5 years old, 5 - 17 years old, or 18 and over. I can do this with a bucket field. I click "Create New Bucket Field," select the field "Age" to bucket, and make my categories based on "Age." Now I can group and count all clients by their "Age" buckets.
Example B (Picklist Buckets): Say clients in my program get their subsidies from different sources and we use a picklist to indicate which type of subsidy they have. I have two or three types of subsidy which are very similar and in a report, I want them all grouped together for simplicity sake. I can do this with a bucket field. I click "Create New Bucket Field," select my subsidy field, and put the similar subsidy types together in a bucket. Now, they will appear with the same name when I group by my bucket field.