The model underlying k-means is that all the data is distributed into k hyperspheres. In the simple 2D case, that means drawing k circles around your data points in a X/Y plot such that the inter-group variance is minimized. This is bad because in the real world, data is typically grouped in an elliptical or irregular way.

There are some examples of this at https://stats.stackexchange.com/questions/133656/how-to-unde...

Thank you!