A Dead Pixel is a problem pixel on an LCD screen, commonly a laptop, desktop monitor or increasingly, a TV. Strictly speaking, a Dead Pixel refers to a pixel that does not light up when it is supposed to (it is always off), this isn't a huge problem since a speck of black doesn't stand out in a picture and is lost in the surrounding bright pixels but the term is often used to refer to Bright Pixels as well, these are pixels that are always on and do not turn off when they are supposed to. Before I talk more about Bright Pixels, a little pixel anatomy is in order.
A pixel on a colour LCD screen is made up of three sub-pixels that display red, green or blue colours and are collectively capable of displaying the spectrum. There are different reasons why pixels might become stuck but when they do, it can be the entire cluster of the three sub-pixels that are stuck or just one or two of the cluster, the terminology is a little different. If one or two of the colours are always lit then it is commonly referred to as a stuck pixel and if the entire cluster is lit then it is a bright pixel or sometimes a hot pixel and it will appear white.
Bright Pixels can be highly visible and are quite annoying, I found that unless distracted, my eyes would seek it out on the screen and I would become annoyed all over again, they would ruin a dark scene in a movie or be a conspicuous dot of colour in the middle of a shadow in a game.
Believe it or not, there is an ISO standard for categorising the seriousness of dead pixels, ISO 13406-2 stipulates four classes of monitor quality and the number and type of faults (dead, lit pixels or lit sub-pixels) with a quite complicated matrix for determining which quality class a given screen will fall into. Generally the user doesn't really care about this, manufacturers usually advertise a certain number of dead or bright pixels that they will allow before exchanging the screen, there are the usual lies involved but that's true of the manufacturers interpretation of the ISO standard too.
Detecting and fixing a Dead Pixel
If you have a TV then I can't help you very much except to suggest that you can probably find a video/DVD or something which will do what you need, your TV may have a test-pattern built in or better yet, hook up a laptop to it, it will be obvious from the computer section what you need to do. Sorry.
On a desktop or laptop monitor, you need to display a screen with a single uniform colour, there is an excellent and simple utility called Dead Pixel Buddy that can be found all over the net and specifically here. You want to display screens of entirely black, white, red, green, blue and a composite colour (yellow is fine), display these one at a time and any dead pixels (of any type) will be quite obvious.
This brings us to the fixing of the pixel. Not all dead pixels can be fixed but if it can, here's how it might be managed.
Method One: Your utility for detecting a dead pixel will probably (certainly, if you use Dead Pixel Buddy) have a mode for flickering through different colours rapidly, leave it running for a while and see what happens, this is something to do with hitting the pixel with electrical pulses until one makes it through but you'd need to be an electronic engineer to understand the specifics and I'm not.
Method Two: Massage. Yes, you read that right. Taking a soft cloth that won't scratch the screen, rub lightly on the dead pixel. If it doesn't clear immediately then power down the monitor, apply light pressure and then power up the monitor before removing the pressure. The exact reasons why this works aren't apparent to me though Wiki says something about letting liquid get into the individual pixels. That doesn't sound quite right but a while back I did fix a dead pixel this way so I'm not arguing with the specifics, be careful though as excessive pressure might actually cause dead pixels.
Method Three: There isn't one that I know of, there is a lot that can simply be defective and can't be fixed by any simple method, these are relatively uncommon though.
Fortunately, dead pixels are becoming less of a problem as manufacturing processes improve and though they were once extremely common due to the complexity and engineering problems involved with colour LCD screens, several manufacturers now offer zero tolerance on pixel faults (possibly only at purchase time but it is still a marked improvement).
Tom's Hardware: http://www.tomshardware.com/2003/03/19/penalty/index.html
Laptop Showcase (Dead Pixel Buddy): http://www.laptopshowcase.co.uk/downloads.php?id=1