A Geometric Brownian Motion is a Brownian Motion with a drift. It is determined by:
\begin{equation} \dd{S_{t}} = \mu S_{t} \dd{t} + \sigma \dd{S_{t}} \dd{W_{t}} \end{equation}
where, S_{t} is a Geometric Brownian Motion, \mu is its drift, \sigma the volatility, and W_{t} a centered Brownian Motion.