Heating a ferromagnetic material lowers it coercivity -- the heat softens it and makes it less magnetically "springy". And if heated enough it fully loses its magnetization.

So, to write, zap the area with a laser to heat it up. The coercivity is lowered. This lets a weaker magnetic field work to magnetize the area. This allows packing more densely, as the weak field will not affect the neighbouring cooler and higher coercivity regions.

(I think.)

This is not the first time lasers have been used to write to magnetic media. Magneto-optical discs (e.g. Sony's MiniDisc) were erased using laser heat. (MO discs also were read with laser, the ferromagnetic material used had different optical properties depending on magnetization.)