nu controls the normality or, if you prefer, the “fatness” of the tails. As nu approaches infinity, the Student t approaches a normal distribution. As nu decreases (nu must be > 0), the tails become much fatter than would be expected under a normal distribution.
Whether you adjust sigma or nu depends on what exactly you are trying to achieve and adjusting one likely means adjustments in the “opposite” direction of the other (e.g., fatter tails mean you can shrink sigma). Often (but certainly not always), both sigma and nu are left as free parameters so that the data can determine how this tradeoff is resolved.