Alerts for when the washer finishes its cycle. Reminders on when to do a tub clean. More detail when certain errors or anomalies are detected. Additional wash cycles for special load/fabric types that don't fit on the dial.I have used the internet connection on my washer for all of these things and it has been very useful.
The HP you mention still exists today as Hewlett-Packard Enterprises, a separate company from HP Inc, which is the consumer-facing brand. It's very similar to what Motorola did in splitting into enterprise and consumer companies.