What do they mean they play on online server i dont understand
It means that you are connectet throgh Internent: Your Computer-router-Internet-Valorant Servers. Plus the servers could be owned by a third party company and they rent them. Anyway the servers are physically located where Riot or the other company operates. So the packets have to travel from your location to your internet provider servers to the Valorant Servers, they all been located in different places.
When we talk about LAN, the servers are local and you don need to connect to Internet.
EU_quiet [#6]It's not LAN servers... there's a Lan client given out to pros who have to play Lan that allows players to play on what we would call a local area network
There is still a LAN server. Someone still needs to host a server on that LAN, which is typically done on a separate machine (for competitive integrity).The client just allows them to play offline rather than exclusively over the internet to Riot's cloud-based servers.