Internal project constraints would typically be resource related. For example, if project team members are committed to supporting more than one project, they have some limitation on the number of hours that they can support your project. Also, your project may utilize an operations factory, laboratory, or equipment resource that is shared by the organization. The Project Manager must work within the constraints of the availability of that resource.
External constraints can come in many forms. Customers may have constraints on the amount or timing of funding provided to your project. This would constrain the schedule and the way that resources are applied to the project.