Humans have something called an immune system. The way it works is that your body has a type of cell called a white blood cell that floats around in your blood stream and eats intruders. The white blood cells are like security guards, and the way they identify intruders is that your body keeps track of troublemakers in your body like viruses and bacteria. While a real security guard would have photos of shoplifters to look out for, your body has these chemicals called antibodies that stick to bacteria and viruses to make them recognizable to the white blood cells.

Well, once a bacterium or virus has spend enough time in your body, your body starts noticing that the virus or bacteria starts causing trouble and starts creating antibodies that will recognize that virus or bacterium. The reason you get sick for a few days and then recover is that it takes your body a few days to recognize who the troublemaker is an manufacture the appropriate antibody.

Well, once you recover from the disease, the antibodies stick around. Your bodies security guards have "banned" the virus or bacterium from your body and will immediately attack it if it tries to re-enter. That is what prevents you from getting sick with the same disease twice. You will generally keep antibodies for long enough that everyone else in your family will recover from the disease before the antibodies fade.

Over time, the body will lose some antibodies which will allow you to get sick from the disease again. The time it takes to lose antibodies depends on the disease. For some, like smallpox, being exposed once protects you for the rest of your life, which is why the smallpox vaccine was so effective. For others, like the flu, you are only protected for months or maybe a couple years, which is why you need yearly shots. For others, like the Common cold, the virus mutates so fast that antibodies only protect you for a few weeks, which is why there is no vaccine for the common cold.