A modem is a device that lets you connect your computer or network to an external system, such as the phone network or the television cable system.
In a typical computer, this is the part that you look at, where everything is displayed for you. It may be similar to a TV screen, and some monitors have touch capabilities, which means that the screen may react to your touch, passing your gestures back to the programs being run.
A mouse is a device that is used for moving your cursor around on the screen. It is used to point at items on the screen so that you can select and use them. You move your mouse around on your desk, and that movement is sensed by the mouse, and details of the movement is sent to the computer. A mouse may have no buttons, or it may have many. By clicking the buttons you can indicate certain actions that you wish to take. A touchpad is often used on laptops instead of a mouse.
A network is a collection of devices that have been linked together. They will usually be related to one another, perhaps by being within the same household. They may be connected through the use of wires (Ethernet) or by wireless.