What does the eth0 interface name mean in Linux?

Your assumption is correct.

The names however can be set/chosen by the user or the operating system that you are using. eth0 and eth1 is used because it's more intuitive than choosing an arbitrary name because "LAN cable" connection, like you said is Ethernet (hence the eth in eth0, eth1). Similarly when you connect to WiFi, it's "WirelessLAN" (hence the wlan in wlan0).

eth0 is the first ethernet interface, any additional ethernet interfaces would be named eth1, eth2, etc.