Remote: Some advantages fo using a program or an app which uses a remote server is data is always up to date and backed up on the server, the developer can update the app instantly for all users without requiring downloads and it is easy to share and collaborate while interacting with data.
Local: ome advantages of using a program with an app which is local would be it works without connection, the data never leaves the device better privacy. It is gernerally faster as there is no waiting for network requests along with it being more secure.
It might be useful to run a server on the computer to develop web applications before putting them online, creating a personal homepage or interal tool for own personal reasons or learning web develppment safely without exposing anything to the internet.
