At bottom, WiiConnect24 is ultra simple: it's the feature of the Wii system that allows it to check for game updates, messages, and other items online. But that simple description can be fleshed out quite a bit.
Since it is in essence an Internet connection (that's where the game updates, messages, and more come from) it relies on underlying mechanisms. One of the more important aspects is the Wii's built-in Wi-Fi support. Wi-Fi allows the Wii to wirelessly connect to the Internet.
There are a few different ways to support that connectivity. One is to make use of a wireless router you have already in place in your home computer network. If you don't have that as part of your network design, you can take advantage of the Nintendo Wi-Fi USB Connector. This small device plugs into your computer's USB port and acts like a mini-wireless router for a system that is hard-wired to the Internet.
Once your Internet connectivity is established, using WiiConnect24 is straightforward. It enables any Wii console to remain connected to the Internet 24 hours per day (hence the name) while in standby mode. In that mode it's possible to receive the game updates, messages, and more referred to above. Forecast Channel and News Channel both use WiiConnect24 to receive up-to-date information, for example.
There is a potential problem with that feature that has affected some Wii consoles. Wi-Fi connectivity can produce excess heat, the enemy of all electronic systems. In standby mode with WiiConnect24, the Wii uses more power, nearly 10 watts as opposed to just a bit more than 1 watt without it. When the internal temperature becomes too great, chips misbehave, sometimes even suffering permanent damage.
It's rare, and it's pretty easy to minimize the probability of that happening.
Early victims of the problem suspected it was WiiConnect24 itself creating the risk. But that's just a software element and so it can't produce heat. Others suspected the GPU (Graphics Processing Unit) was at fault, since one way the problem shows up is through random darkened pixels on the screen. But that's a side-effect, not the underlying cause. With the system in standby mode, there's no way a graphics unit can produce excess heat.
After much research, Nintendo found that the Wi-Fi components inside the console were responsible for the problem for those few systems that experienced it. Fortunately, the cure is straightforward.
Despite the name, few systems are designed to be on 24 hours per day, 365 days per year. Those (like PCs and Macs) have special software, fans, and more that help reduce heat. The heat is produced by the chips themselves as electricity passes through them all day. The Wii, too, has a fan and vents to expel heat and cool the components, but they have to be allowed to work properly. Keeping your Wii in a well-ventilated area with none of its vents covered or too close to a wall can head off problems before they occur.
If that doesn't do the trick as you can detect by touching the side of your Wii and finding it excessively hot to the touch, external cooling fans are an option. In the worst case, which isn't very bad after all, just completely power off your Wii once in a while. Daily power-off is rarely needed, but that's an option, too. The Wii boots up quickly.
Once you've established your WiiConnect24, you'll be able to get updates for Animal Crossing, Big Brain Academy, Mario Kart, and many more games. You'll be able to tell that your feature is working by the yellow color of the Power LED (red means off). Once you receive updates the Wii Optical Drive will glow blue and/or flash depending on your firmware level or what sort of data has been received.