Finally, it's here.
A viewfinder is the part of a camera that displays the image to be taken, and is only visible when the camera is held to the photographer's eye. Oppositely, some cameras (and all camera phones) only display the image on a main LCD display, which the photographer can view at arms length instead of having to hold the camera to their eye.
The Camera Viewfinder
Most serious cameras have a viewfinder, whether it is an electronic display or an optical prism. The viewfinder must be held up to the photographer's eye to be seen, as it is built into the camera itself, as opposed to a LCD display or focusing screen that is visible from a distance, such as the ground glass of a large format camera, or the live view feature on a DSLR or mirrorless camera.
For many types of photographers, from action sports shooters to candid portrait shooters, having the camera raised to the eye is beneficial in that it allows the photographer to be fully involved in the viewing of their image before it is clicked, undistracted by other surroundings, as well as being discrete in certain ways.
The Optical Viewfinder (OVF)
Most optical viewfinders use a mirror, a focusing screen, and a glass or mirror prism to allow a photographer to see through the lens itself. Some cameras have different viewfinder designs, such as rangefinder cameras, which do not actually look "through the lens" (TTL) but instead have a separate viewfinder window.
The advantages of an optical viewfinder are that the "real world" is represented exactly as it is, and exactly as it happens. An optical viewfinder can be viewed even while the camera is turned off, and consumes little to no battery power while the camera is on.
A wealth of information can be displayed in an optical viewfinder, including exposure settings, metering information, flash and white balance information or warnings, and focus confirmation for manual focus lenses.
The Electronic Viewfinder (EVF)
Electronic viewfinders, also known as EVFs, use the image sensor itself to record what the sensor is seeing, and play it back on a digital display inside the viewfinder for the photographer to see.
The advantages of an electronic viewfinder are that the "final image" is represented exactly as it will be captured, which is known as "what you see is what you get" or WYSIWYG. This aides the photographer in both eliminating technical mistakes, (such as accidental underexposure or incorrect white balance) and also in creative artistry, by showing what creative effects will look like such as dramatic, intentional high-key or low-key exposures.
There are many other advantages to an electronic viewfinder, including the ability to display much more information such as a live histogram, focus peaking, exposure warnings for highlight or shadow clipping, and other things.
The disadvantage of an electronic viewfinder is that the electronic display has historically had a slight "lag time", or delay, between the image being captured on the sensor and replayed in the viewfinder. This means that if you see a critical moment happen in the EVF, it has already happened in the "real world".
However, this lag time has largely been eliminated from the latest generations of EVFs, and the image seen in the viewfinder is coming from the sensor almost instantaneously. Unfortunately this playback speed, as well as the ever-increasing resolution of the latest electronic viewfinders, comes at another price: battery consumption. Because EVFs have even higher resolutions and refresh rates than most rear LCD displays, they consume battery power even faster than ordinary live view (LV) on any type of camera, whether optical or electronic viewfinder. (Fortunately, the latest mirrorless cameras with high-end EVFs are also developing higher capacity batteries as well, and more efficient power consumption is actively being developed by camera companies with high-end electronic viewfinders.)