We have that $\xi_n\sim\mathcal{N}(0,1)$, and these $\xi_n$'s a independent.
The above equation is the Euler-Maruyama discretisation of the stochastic differential equation $$\mathrm{d}X_t = -X_t\mathrm{d}t + \sqrt{2}\mathrm{d}W_t,$$ where $X_t$ is a continuous time stochastic process and $W_t$ denotes a Wiener process (standard Brownian motion).