There is a saying that the cloud is just somebody else's computer, but with your own server, it can be your computer. You always need to trust the admin or company of any server/cloud service you use to not abuse you in some way, but if you are the admin, you only need to trust yourself.

Some of these server apps are made available to others by hosts of servers. The more people hosting servers for their friends and family, the less we all rely on the big central services.

I will let you lookup the definition of localhost. You will need to learn some networking if you decide to host your own services, and I encourage you to do so. It is fun and empowering.