Wat is SVI parametrisation?

The SVI parametrisation (stochastic volatility inspired) of a smile writes the total implied variance of one expiry as

with $b\ge0$, $|\rho|<1$, $\varsigma>0$ and $a+b\varsigma\sqrt{1-\rho^2}\ge0$ (so that the minimum of $w$ is non-negative). The parameters have a shape each: $a$ the level, $b$ the angle between the wings, $\rho$ the rotation (the skew), $m$ the horizontal position of the minimum, $\varsigma$ the smoothness of the vertex.