So there are some limitations to k-means clustering. Here they are:

1. Choosing K: First of all, we need to choose the right value of K, and that's not a straightforward thing to do at all. The principal way of choosing K is to just start low and keep increasing the value of K depending on how many groups you want, until you stop getting large reductions in squared error. If you look at the distances from each point to their centroids, you can think of that as an error metric. At the point where you stop reducing that error metric, you know you probably have too many clusters. So you're not really gaining any more information by adding additional clusters at that point.
2. Avoiding local minima: Also, there is a problem of local minima. You could just get very unlucky with those initial choices of centroids and they might end up just converging on local phenomena instead of more global clusters, so usually, you want to run this a few times and maybe average the results together. We call that ensemble learning. We'll talk about that more a little bit later on, but it's always a good idea to run k-means more than once using a different set of random initial values and just see if you do in fact end up with the same overall results or not.
3. Labeling the clusters: Finally, the main problem with k-means clustering is that there's no labels for the clusters that you get. It will just tell you that this group of data points are somehow related, but you can't put a name on it. It can't tell you the actual meaning of that cluster. Let's say I have a bunch of movies that I'm looking at, and k-means clustering tells me that bunch of science fiction movies are over here, but it's not going to call them "science fiction" movies for me. It's up to me to actually dig into the data and figure out, well, what do these things really have in common? How might I describe that in English? That's the hard part, and k-means won't help you with that. So again, scikit-learn makes it very easy to do this.

Let's now work up an example and put k-means clustering into action.