A private IP address is used within a local addressing arrangement rather than being directly routable as a public internet destination. Such addressing lets a home network organise its devices internally. A router or another gateway commonly connects that local network onward, often using address translation for IPv4 internet communication on behalf of local devices.
A practical example
A television and phone can each have a different private address while using the same home router for internet access. That makes it possible to identify the local devices without assuming that an outside service sees those same internal addresses.
A common misunderstanding
Do not paste a private address into a remote service field merely because it appears in the device's network menu. A local device address is different from the service's server or playlist address.
Related terms
Stable technical definition. Editorial approach