Overfitting, in a nutshell, means take into account too much information from your data and/or prior knowledge, and use it in a model. To make it more straightforward, consider the following example: you're hired by some scientists to provide them with a model to predict the growth of some kind of plants. The scientists have given you information collected from their work
with such plants throughout a whole year, and they shall continuously give you information on the future development of their plantation.
So, you run through the data received, and build up a model out of it. Now suppose that, in your model, you considered just as many characteristics as possible to always find out the exact behavior of the plants you saw in the initial dataset. Now, as the production continues, you'll always take into account those characteristics, and will produce very fine-grained results. However, if the plantation eventually suffer from some seasonal change, the results you will receive may fit your model in such a way that your predictions will begin to fail (either saying that the growth will slow down, while it shall actually speed up, or the opposite).
Apart from being unable to detect such small variations, and to usually classify your entries incorrectly, the fine-grain on the model, i.e., the great amount of variables, may cause the processing to be too costly. Now, imagine that your data is already complex. Overfitting your model to the data not only will make the classification/evaluation very complex, but will most probably make you error the prediction over the slightest variation you may have on the input.
Edit: This might as well be of some use, perhaps adding dynamicity to the above explanation :D