Mean-reverting stock model and its effect on calls

A stock is modelled by $dS=\alpha(\mu-S)\,dt+\sigma S\,dW$. How does it behave, what do $\alpha$ and $\mu$ represent, and how do they change the price of a call option?

They do not affect the call price. The drift pulls $S$ towards the level $\mu$, with $\alpha$ setting the speed of reversion, and the noise is proportional to $S$. But a traded stock can be hedged, so under the risk-neutral measure its drift is replaced by $rS$ and only $\sigma$ (and $r$) enter the price. The real-world drift parameters change forecasts and P&L, not the no-arbitrage value.