Deliquescence is a process whereby the pileus liquifies itself to allow the spores to escape. The pileus starts liquifying itself at the margin, leaving the margin tattered and flaring (above the liquifying zone, the pileus is usually straight vertically). Often there is a reddish zone at the transition between the white immature gill tissue and the liquifying tissue which is black with the mature spores.
In some species, the process is a little different: only the gillsdeliquesce, leaving a thin, almost transparent layer of the pileus behind.
I used to think that the black, inky liquid that runs off was the main method of spore dispersal for these fungi. But I read recently that the spores mostly get dispersed in the air, like other fungi: they drop off just as the pileus liquifies around them. It is only a small percentage of the spores that get trapped in the liquid.