I have 100 data points, observed on 15 variables. I want to cluster my 100 observations, but I am unable to visualise 15-dimensional clusters in MATLAB.
Calculate distances between data points, as appropriate to your problem.
Then plot your data points in two dimensions instead of fifteen, preserving distances as far as possible. This is probably the key aspect of your question. Read up on multidimensional scaling (MDS) for this.
Finally, color your points according to cluster membership.
I have successfully used a Self-Organizing Map (SOM) in the past for this task. It is a kind of Neural Network with some relation to Clustering, with significant advantages over them for some specific tasks. The main advantage (to me) is that it is an unsupervised method, meaning that you can apply it even with unknown classes in your data. If you know your classes, you could use this information to color the distinctive clusters/regions obtained in the output map.