In just four lines, the speaker describes a grim morning and a strange way of coping with it. The air is "rank," and the speaker says they "batten on" two things: ash and rot. "Batten on" means to feed greedily, so these are not things to be avoided but sources of nourishment. The dashes offer a surprising key. The ash is "my wife," and the rot is "my diary." Read closely, the poem suggests the wife may be dead, cremated perhaps, though the text never says so outright. The diary, meanwhile, is decaying on the page, or maybe it is simply the record of decay.
The last line, "break down the day," works two ways. It sounds like the speaker is breaking the day into pieces by writing about it, but it also echoes the way rot breaks things down. Writing and decomposition become the same act. The mood is bleak, intimate and oddly calm. Grief isn't shouted here. It is turned into daily material, something to chew on and write about.