The equation
amp*np.exp(-(t_back-t_start)/rate)+b1
describes the average trend which relate the predictor variables (t_back I assume in this case) to outcome variables which is the observed. However the data will not exactly match this trend, more likely it will be distributed with some noise around this data. sigma in this particular model represents how much noise you allow. Normally, if there is enough data this is also left as a parameter to be estimated with something like this
noise = pm.HalfNormal("noise", 5)
Here I wrote 5 arbitrarily, it should be chosen to represent the natural scale of data in your case but this is still much more flexible than trying to guess an exact sigma for your problem. If you standardise your data in some way, this is generally close to 1. You might get a bit more in depth idea on the choice of particular priors for sigma here:
Prior distributions for variance parameters in hierarchical models