I haven't done much with nmlefitsa, so I don't have much experience with it. As a general rule however, COVB (the covariance matrix of the parameter estimates), provides one rather important bit of information on the parameters themselves: it allows you to calculate the confidence intervals on the parameters.
With Beta a column vector of the parameter values, and CovB the covariance matrix, the 95% confidence intervals are given by:
CI95 = [Beta-1.96*sqrt(diag(CovB)) Beta+1.96*sqrt(diag(CovB))];
The 1.96 value is the ‘critical value’ (the z-statistic or z-score) corresponding to the 95% confidence interval:
cv = norminv(0.975, 0, 1);
The usual interpretation of the confidence intervals on the parameters is that if the confidence interval for a particular parameter includes zero, that parameter is not needed in the model.