The term "shade grown" is a heavily marketed term meant to conjure up positive feelings about the way certain coffees are grown. To grow coffee at scale, large farms have had to breed ever more hardy plants, and part of optimizing yield is to grow coffee as a monoculture (think fields as far as they eye can see filled only with low-growing coffee shrubs). Unlike plant development in the wild, monocultures cause real problems for other species living in the ecosystem, who rely on the physical and chemical variety of flora for their habitats (everything from sources of food, to places to nest, to cover from predators). So the idea that farms will manage their monocultures in the direction of more biodiversity is a Good Thing, that's helpful for, among other creates, birds, who need certain conditions to nest.
All of that said, there are a few catches. First off, in many places, especially smaller farms, coffee is by definition grown in a more biodiverse context, with the "shade" of other plant specifies a natural part of the landscape. This is part of why we prefer working with roasters who work directly with smaller-scale farms, and purchase high quality micro lots. But there's another aspect to the marketing angle that's seeped into conventional wisdom: the term suggests, insidiously, that growing coffee in the shade somehow results in better coffee. That suggestion is just for the birds (pun intended), and coffee labelled "shade grown" literally says nothing about the nature of the product you're buying, except to the extent it might describe either intentional or accidental features of the farm.