Stock price modelling under binomial tree model?

In binomial tree model, the stock price is modelled in the form of $S_{k\delta}=S_{(k-1)\delta}\exp(\mu\delta+\sigma\sqrt\delta Z_k)$ , where $\delta$ is time invertal between two observations $S_{k\delta},S_{(k-1)\delta}$ , $Z_k=1,-1$ for upward and downward scenarios of the stock price change. I noted some illustrations of variance and mean to explain why the model is set in the form, but I cannot find more explicit explanation. Could someone help?