Is there a concept of inheritance for Kubernetes deployments?

Helm is what many people are using for this. It let's you create templates for kubernetes descriptors and pass parameters in to generate descriptors from the templates.

There are other tools out there which can be used to generate variations on kubernetes deployment descriptors by injecting parameters into templates. Ansible is also popular. But Helm is closely connected with the Kubernetes CNCF and community and there's a good selection of official charts available.

EDIT: If the aim is to enable different deployments (e.g. for dev and prod) using a single docker image then that's probably best handled with a single chart. You can create different values files for each deployment and supply the chosen values file to helm install with the --values parameter. If there are parts of the chart that are only sometimes applicable then they can be wrapped in if conditions to turn them on/off.

On the subject of inheritance specifically, there's an example in the helm documention of how to take another chart as a parent/dependency and override its values and I created a chart earlier that you can see in github that includes several other charts and overrides parts of all of them via the values.yml. It also shares some config between the included charts with globals. If you're looking to use a parent to reduce duplication rather than join multiple apps then it is possible to create a base/wrapper chart but it may turn out to be better to just duplicate config.

EDIT (180119): The alternative of Kustomize may soon become available in kubectl

You may also want to check Kustomize. It provides some support to write your yaml manifests in hierarchical form, so that you don't have to repeat yourself.