As a network engineer, I get these kinds of questions all the time.
Answering what a modem is is easy, but explaining how it works made me take up my textbook from college to refresh my memory. But after some reading, I will now answer that question as well.
In this article I will explain:
- What a Modem is
- The different types of Modems
- How a Modem works
- Is a Modem Necessary?
Types of Modems
There are three types of Modems, and these are categorized by the type of service they are receiving.
A Cable Modem connects to your ISP using coax cables, the same cables that bring your television to your home.
The pros with this are that it is capable of handling more data. Which enables it to support higher internet speeds.
The con is that since you share cables with your neighborhood. Your internet connection might get worse during the busy horse when everyone is looking at television and uses the internet. 
A DSL modem connects to your ISP provider using your telephone cable as its medium for providing your home with the internet.
The pros with DSL modems is that it is very accessible for everyone. This is because it uses the same infrastructure as telephones do. Furthermore, it is also stable. Since every house has its own line, your neighbors’ activities will not affect your internet speed.
The con with DSL is that it has a lower speed than Cable. This is because the cables it uses are made for telephones which don’t need as much data as televisions.
It’s also the type of modem used for internet calling (VOIP). 
These kinds of modems are used at remote places and on boats.
This is because it is slow and hard to come by, and also very expensive and bad weather will disturb it.
How a Modem Works
A modem is very complex, and even as a network engineer I don’t understand all the parts and functions inside a modem.
These key components are:
The turner receives the data from the cable. Sometimes it has a splitter that separates the internet data channel from the phone data or the TV data. The Turner then passes the data to the demodulator
A Demodulator takes the analog signals it receives from the ISP and converts it into digital signals (same as binary signals). This is so that the hardware in your home network will be able to understand the data they are receiving.
A Modulator does the opposite of a Demodulator. It takes digital signals and converts them to analog signals that can then be sent back to your ISP, or in other words upload data to the net.
4. Media access control (MAC)
The MAC sits in the middle of the modem and works as an interface between the hardware and the software portions of various network protocols (protocols are the rules hardware uses to communicate). This MAC is more complex than in other hardware and will also have an assigned CPU for some of its functions.
The microprocessor role depends on the network, but in a home network it functions as the support to the MAC, it will for example pick up a lot of the slack the MAC leaves.
Is a Modem Necessary?
Yes, If you want the internet in your home a modem is necessary. But there are some options you can choose from when building your home network.
You need a modem, a router, and a switch to get a well-working home network. But you don’t have to buy three different devices, you can for example buy one modem, and one router with an inbuilt switch. Lowering it to two devices.
You can even take it a step further and buy all one packet, a router-modem combo. It has a modem, a router, and a switch built-in, this is also called a Gateway.
The pro with a Gateway is that it is more convenient and easier to handle and set up. The con is that if any of the parts break or are in need of an upgrade you need to change all three. While if you have it separate you can change one when necessary.
The Bottom Line
A modem is important for your home network. It works as a translator that allows the rest of your home network to understand your ISP’s signals.
If you are thinking about buying a modem and are not sure what to get I have written about the best ISP approved and compatible modems, that you can check out if you’re uncertain what to get.