Origin: Shakespeare’s ballad seller Autolycus in The Winter’s Tale IV, 2. The saying refers to making use of every single thing and/or every bit of information.
Here are two modern examples, in context:
Professional writers are magpies, snappers up of trifles. They keep notebooks, cuttings, jottings, selections from authors new to them.
Historians, like anthropologists, tend to be particularists, snappers up of what sociologists, political scientists and economists, all grand generalisers, think to be matters too trifling for their consideration.