With Ethernet library, the board can upload data to local network and I can input the IP address (192.168.1.71) to visit it.
However, non local network user can't visit this data. Can the board upload data to the Internet and then everyone can visit it?
Yes, that is what the Internet of Things is all about. Somebody else hosts it, you control it, everybody else can look at it.
There are several different providers.