What do modems do?
Modems are devices which provide a direct connection to the Internet. On it's own, your router doesn't connect to the Internet - it needs a modem as well.
In fact, it's called a modem because it modulates analog signals - what travels through the undersea wires to connect to servers - into digital information which computers can read. So you can think of the modem as the interface between the Internet and your router.
When you send/receive information on your devices, you do so using digital binary information. Binary basically refers to 0s and 1s, but we'll save the computer science course for later. To connect to servers, that information needs to travel through high-speed wiring. Unfortunately, wires can only transmit analog signals.
To fix this issue, your modem will transform your information into an analog signal which gets sent to your ISP, and information that comes to you is transformed back into useful digital information that your devices can read.
If you have a slow modem, your entire network will be slow as a result. So it can be worthwhile choosing a modem which supports your internet plan speeds.