These days the word ‘router’ either has people thinking about internet connections or loud high speed hand held machinery! (My particular router plane predates both... early part of the 20th century).
Router planes were used for accurately leveling all kinds of recesses for example halving joints, grooves, hinge mortises and stopped rebates or grooves where a chisel cannot reach. Today you can do all of those things and more with a hand held electric router, but sometimes it’s nice not having to wear ear protection and sometimes the router plane is faster to set up!
Router planes have been around for a very very long time and were originally made from wood! Another commonly used name for this tool is ‘Grannies Tooth’ due to its single blade poking out!