Showline is a term used by breeders of animals to define animals bred from stock that are bred for showing, as opposed to animals being bred for working purposes. Also, there is quite a difference between show or working lines and show or working animals (i.e. an animal can be a show champion but come from working lines).
It can also be used for describing certain marketing activities such as tradeshows, exhibitions and events.
References
Show line Wikipedia(Text) CC BY-SA