What is a network switch, and do I need one?
A device that connects wired devices on the same local network, forwarding each frame only to the port where its destination actually is. Most homes do not need one; most homes that run out of router ports do.
What it does, precisely. A switch learns which device sits on which port by observing the hardware addresses of traffic passing through, and builds a table. When a frame arrives it consults that table and sends it out of one port only. This is the difference from an obsolete hub, which repeated everything to every port, wasting bandwidth and creating collisions.
Why your router already is one. A home router is several devices in one box: a modem or network interface, a router, a wireless access point, a firewall — and a small switch providing the Ethernet ports on the back. Adding a switch simply extends those ports, and traffic between two devices on the same switch never reaches the router at all.
When one is genuinely useful: more wired devices than router ports; a single cable run to another room feeding several devices there; connecting a games console, television and streaming box behind the television; reducing Wi-Fi congestion by wiring anything that does not move; and connecting access points for a wired mesh backhaul.
What to look for:
Speed. Gigabit is the sensible minimum; 2.5 gigabit matters only if your internet or internal transfers exceed a gigabit.
Unmanaged versus managed. Unmanaged switches need no configuration and are what most homes want. Managed switches add VLANs, port monitoring and link aggregation — useful for segregating smart home devices or a guest network, and unnecessary otherwise.
Power over Ethernet, if you are feeding access points, cameras or doorbells over the same cable.
Fanless, for anywhere you will hear it.
What a switch will not do: improve your internet speed, extend Wi-Fi, or route between networks. It moves frames within one network, nothing more — which is exactly why it is cheap and reliable.