It's a common acronym across several different networks, especially in the early Internet. I am not exactly sure but I believe it stands for Network Information Center. FUNET is the Finnish UNIversity NETwork, i.e. the early research network that first connected Finland to internet when it was still mostly a tool for researchers to connect and share data.
NIC.FUNET.FI would've been the central directory server where you found other services on offer across the larger FUNET, the hub. Mind you search engines would not really exist for several years in 1990.
