Definition
This idiom is used to question why someone is doing something themselves when they are already paying someone else to do it.
You paid for a gardener, but you're mowing the lawn yourself; why keep a dog and bark yourself?
Since you hired an accountant, you should let them handle the tax filing; why keep a dog and bark yourself?
The company has hired a consultant to handle this project, but the manager is doing everything himself; why keep a dog and bark yourself?