Jenkins - Scripted Pipeline - Input String
After some more research I found the answer:

  def coreImageTags = input(
    id: 'coreImageTags', message: 'Enter a comma separated list of additional tags for the image (0.0.1,some-tagname,etc):?', 
    parameters: [
      [$class: 'StringParameterDefinition', defaultValue: 'None', description: 'List of tags', name: 'coreImageTagsList'],
    ]
  )

  echo ("Image tags: "+coreImageTags)


Important note

It is stated in the documentation but I want to point it out specifically: If you copy/paste my solution here, coreImageTags will contain a string directly. If you do multiple parameters like so:

    parameters: [
      [$class: 'StringParameterDefinition', defaultValue: 'None', description: 'List of tags', name: 'coreImageTagsList'],
      [$class: 'StringParameterDefinition', defaultValue: 'None', description: 'Something else', name: 'somethingElse'],
    ]


You will not get a single values but an array of values:

  echo ("Image tags: "+coreImageTags['coreImageTagsList'])
  echo ("Image tags: "+coreImageTags['somethingElse'])


The following posts will help:

stackoverflow.com read-interactive-input-in-jenkins-pipeline-to-a-variable

CloudBees - Pipeline-How-to-manage-user-inputs

A list of classes you can use in this way and what they do is in the Jenkins Input-Step documentation:
Pipeline - Input Step