Tempering eggs is a critical culinary process, especially when it comes to making puddings, custards and other similar recipes. Eggs are tempered when a hot liquid (usually milk) is carefully streamed into them, bringing the eggs up to a very high temperature without cooking them. When properly incorporated, eggs have thickening properties that will help bring a custard to the appropriate consistency. This process is trickier than it sounds, since eggs cook a lot more easily than other ingredients and the last thing you want to add to a pudding is scrambled eggs!
To temper an egg, or multiple eggs, you need a large bowl and a whisk. Give the eggs a brief whisk in the bowl. Take your hot milk mixture and, working with just a few teaspoons at a time, pour it into the eggs as you whisk continuously. Adding the milk in this slowly prevents the eggs from being coked instantly from exposure to heat. Keep adding the milk in very small increments until all of it has been added. Strain the egg mixture back into your saucepan, removing any bits of egg that might have gotten cooked, and proceed with your recipe as written.
Now, you could try and just stream in your eggs (or egg mixture, as seen in this banana cream pie recipe) to the hot milk mixture to save time and dishes. This is not a good idea. When your egg hits that hot liquid, even if you whisk very fast as you work, it will cook almost instantly. In a best-case-scenario with this method, you will end up with a lump or two in your finished pudding/custard. In a worst-case scenario, you will end up with a saucepan full of scrambled egg pudding. If things go awry in the previously described method, you’ll only have to throw out a small portion of your hot milk mixture and start over with new eggs, saving a lot of time and a lot of batter.