If you read the title, you may be thinking, "what the heck is that?" But if you break it down, you can see the word video, so you might think 'picture.' You can see laryngo and think 'larynx/voicebox.' Strobe might make you think of light. And according to dictionary.com, scopy "indicates viewing or observation."
So a videolaryngostroboscopy is a technique used to examine the vocal chords. Speech pathologists who specialize in voice may conduct these evaluations quite frequently. The main component of the equipment used for this assessment is a gadget called an endoscope. This picture, from www.performancevoice.com shows one in use.
The physician is putting the endoscope into the patient's mouth. The endoscope has a small camera at the end that is slightly angled so that it can see the vocal folds more easily. The camera is connected to a fairly large screen so that the physician can easily see the tissues.
The endoscope is fun to use because it is controlled by foot pedals, as both hands are needed for maximum control of the endoscope. One pedal turns on the regular camera light, one turns on the strobe light, and other pedals control the recording of the video. Now, I mentioned a strobe light (thus the term "stroboscopy"). The strobe light is used to view the movement of the vocal folds more easily. Vocal fold movement is really quick--faster than what the eye can detect. So to get a better picture of how the folds move, we use a strobe light. This tricks the eye, providing a slow motion effect.
So here is what you will see when you use the endoscope. The first picture (left) is what the vocal folds look like when they are open (when someone is just breathing). The second picture (right) is what the vocal folds look like when they vibrate (when someone is speaking). If you are interested in an actual video, just search video stroboscopy on YouTube.com and you can find plenty of examples.