I'll assume you have used negative binomial (NB) regression to analyze over-dispersed counts per time unit (e.g. modelling the number of hospitalizations per patient-year of follow-up by having a NB model with a log years of follow-up offset).
If so, the regression coefficients correspond to differences in the log-rate associated with different values of a covariate. Once you exponentiate the coefficient, it becomes a ratio of rates associated with different values of a covariate. Example, if we are in a randomized trial and the covariate is treatment (0=placebo, 1=new drug), then $\exp(\beta)$ is the rate ratio for the annualized rate of hospitalizations for drug compared with placebo. If we the covariate is (continuous) blood pressure in mmHg, then it would be rate ratio by which the annualized hospitalization rate is observed to be higher or lower (=not necessarily a causal effect, but possibly just something that could be a non-causal correlation) per 1 mmHg (or, $\exp(10 \times \beta)$ is that rate ratio per 10 mmHg).
To illustrate this further, here's an example of randomized controlled clinical trial using negative binomial regression and how they reported the results.