If I make some experiment, which I repeat $N$ times, and look at the distribution of the experiment. I would usually expect (and hope) for a Gaussian or normal distribution.

If however my data is T-distributed, what is this saying about my data? What can I interpret from the T-distributed.

I realise this may be a slightly open ended question, but if I may illustrate what I am after by means of example. If I make an experiment and my data comes out as a Rayeligh distribution, I can already say that my data is comes from the absolute magnitude of two components which are both Gaussian distributed.