I am doing a little bit of research on some basic advection schemes, and getting a bit confused - i need to know why an upwind scheme is more numerically stable than the Van Leer scheme. Is it because the Van Leer scheme requires iteration?

I'm not sure I understand your question. The most basic Van Leer scheme is a flux vector splitting scheme which is an upwind scheme. As I recall, flux-vector splitting schemes suffer from being only first-order accurate and requiring homogeneous flux vector functions. They are however fairly stable (with proper care taken at sonic points). What upwind scheme are you comparing to flux vector splitting?