Boysenberries are a plump, juicy berry that come on around the same time as blackberries. Their season begins in early July and runs through mid-August. Recently, they have become more popular in such treats as jams, jellies, and syrups. A sweet, luscious berry that substitutes nicely for most other berries in baking, salad, and dessert recipes. Boysenberries provide iron, calcium, and are low in sodium. Boysenberries, like dewberries and logan berries are a trailing type of blackberries.

Here are some good links for boysenberry recipes and more information.
http://www.oregonfruit.com/oregon_fruit/boysenberry.html
http://www.oregon-berries.com/