Custom objects are a way to represent a relationship that your organization has with something that isn't one of HighLevel's standard objects.
EXAMPLE:
For a veterinarian's business we would be able to create a PET object. That object could have fields like owner, name, type, breed, etc.
We would be able to associate multiple pets to one owner.
We would also be able to associate calendar events (visits/checkups) to the Pet.
ANOTHER EXAMPLE:
Automobile Repair Shop. We would be able to create a CAR object. Fields like owner, make, model, year, color, etc.
We would be able to associate multiple cars to an owner.
We would be able to create an appointment and associate to a car.
BONUS: The ability to trigger off of a custom object. Add custom objects to a pipeline, etc.
BONUS: The ability to have the dynamic object fields available in emails, etc.
I believe these features would push HighLevel past being a marketing platform and into a platform that can be customized for daily operations.