You run a Minecraft server on your network (LAN). You have a second computer, which has the Minecraft client. Using the client computer, you go to the "Multiplayer" menu. It says "Scanning for games on your local network" and searches, but it doesn't find the Minecraft server on your LAN automatically, but it does find the game automatically when you use another computer with the Minecraft client and choose "Open to LAN" from the pause menu. This doesn't make sense, as both games are on the LAN, whether you are using "Open to LAN" on another computer, or running Minecraft server software.
LAN games only show up when made from singleplayer worlds. Servers are different by nature.