Wi-Fi is common for most households but good Wi-Fi is not. Most homes have a single Wi-Fi access point and it may or may not be in the best location for adequate coverage. There is a lot of misconceptions about Wi-Fi products so let's see if I can't clear a few things up for you.
First, we need to go over the basic components of a WiFi network.
The first device in your system is a modem. At its core a modem has a cable going in from your service provider (cable company, phone company etc..). Then a single cable coming out, that is your internet connection.
The second component is a router. The router is the traffic manager of your network. It regulates which devices can be on the network, provides basic security and provides a separation point between two networks, usually those networks are the outside world and your private home network.
The third component is a switch. Basically you can think of a switch as a splitter.
The last component is the Wi-Fi radio. A box that may or may not have visible antennas and may or may not handle both Wi-Fi bands. Bands? Just like your car radio has two bands, AM and FM, Wi-Fi has two bands. 2.4 Ghz and 5 Ghz each with benefits and problems.
All WiFi devices operate on 2.4 Ghz and most operate on 2.4 and 5 Ghz.
These four components can be found either as individual stand alone boxes (rare these days), grouped into a few boxes or all in one.
There are numerous variations to what is shown here. You can add another WiFi AP to any of these configurations. You can add additional switches to an existing network to increase the number of connected devices. You may even have more than one router. However, you can only have one modem unless your router has two WAN ports, which is typically only found on commercial grade products and even then is rarely used outside enterprise level networks.