The Brocken Spectre appears when a low sun is behind a climber who is looking downwards into mist from a ridge or peak.
The spectre is the shadowy figure, the glow and rings are of course a glory centered directly opposite the sun at the antisolar point.
But how is the ghostly figure produced? It is no more than the shadow of the climber projected forward through the mist. All shadows converge towards the antisolar point where the glory also shines. The sometimes odd triangular shape is a perspective effect. The Brocken Spectre is a similar effect to anti-crepuscular rays and cloud shadows.
The spectre sometimes appears to be huge. This is probably caused by the presence of the glory and the mist obscuring more familiar reference points with which to judge its size.