Simplified, the modem is a listening device that can handle incoming packets (modulator-demodulator traffic).
You will need one for dial-up, isdn, dsl, cable, fibre, etc.
Most modems have a built-in way to switch between ports, to get 'this' going 'there' and 'that' going 'over there'.
Sometimes a modem can be put in bridge mode. It becomes more of a 'dumb device' as I like to call it. It does the initial handling of traffic, and then you send it off to the router that's behind it.
A router simplified is a device that can forward traffic to the right device. Adding your own router to your network (modem in bridge mode for example) allows you to spread the workload of the modem, to modem and router. And the router sometimes is even more powerful in hardware to deal with todays wide variety of traffic. Especially in a household with multiple people, all having multiple devices. Using a router with more advanced wifi capabilities and proper antennas can also improve the performance, spread the pressure of traffic through quality of service, dedicate a guest network, or have multiple things like the older 2.4ghz for 5ghz.
I always recommend to ask the ISP if the modem can be set up in bridge mode and if it is allowed to use your own router behind their modem. If so, then get a modern router that's around 150 bucks, and configure it properly. You might just be surprised how it helps your network.