what is the typical purpose of 3 LAN ports on a router ? What kind of usage require more than 3 ports ?
Are LAN ports on routers similar to the capability of a managed switch ?
A router with "LAN ports" (and probably one "WAN port") sounds like a router designed for a specific use case: providing NATted internet access to multiple devices over a connection with one public IP address. These are often consumer or SOHO products.
In this case, the LAN ports will most likely behave as an unmanaged switch. There are of course exceptions. Please be specific if you have a particular device in mind. (Note: consumer grade products are explicitly off-topic here)
A more generic router would just have interfaces, which can be configured in many ways and connected to multiple LANs, WANs and other networks.
Simple. To connect 3 wired devices. Like if you want to connect three PCs via an ethernet cable to your router, you'd use those ports.
Multiple LAN ports on a router can mean two different things:
At my employer's, when we connect spoke sites with dual WAN connectivity (i.e. one Metro Ethernet service by carrier "A", one MPLS based L3 VPN by carrier "B"), we usually deploy routers with at least three ports, to connect...
That A-B cross-link becomes part of the dynamic routing environment of the WAN overlay service (mostly MPLS-o-GRE-o-IPsec) we provide.
That design brought us advantages like:
There's a few catches to avoid (like making sure that the crosslink is never used as transit by other sites or even considered as backbone link), but overall, we've seen improvements in resilience and failover times over our previous FHRP-only based designs.