Organic are made up primarily of the remains of once living organisms.
The most commonly thought of organic sedimentary rock is lithified remains of plant material that forms peat lignite and coal.
However organic sedimentary rocks are not limited to coal. Some limestones consisting of lithified remains of invertebrates such as corals or shell materials are technically organic sedimentary rocks although less commonly thought of as such.
Additionally some shale deposits have such high volumes of organic material e.g. oil shales that contain enough kerogen they can sometimes burn. They also can be argued as being organic sedimentary rocks.