A Wraith data storage device is a small computer memory storage device. Wraith computers will often have interfaces with them.
After shooting down a Wraith Dart during a culling, the Genii managed to retrieve a storage device from it and an interface to access the information was created by Tyrus and his daughter Sora. The device contained information on the Wraith hive ship the Dart had come from, including the Stargate address of the planet it had landed upon for hibernation and data on the planet. In 2004, the Atlantis expedition and the Genii conducted a successful raid to download information from the hive ship's data core onto the storage device to learn more about the hive ships and their locations. Peter Grodin was eventually able to learn from the data, most of which was encrypted, that there were possibly as many as 60 hive ships in the galaxy. According to Doctor Rodney McKay, the data on this device contained more of a "galactic positioning system for ships" than writing or other data. (SGA: "Underground", "The Gift")
During the Genii invasion of Atlantis, one of their immediate demands was that the stolen storage device be returned to them. Doctor Elizabeth Weir retrieved it for Sora and Ladon Radim, telling them that all of the data that they downloaded was still upon the device. The Genii presumably took it with them when they abandoned Atlantis, but what, if anything they learned from it is unknown. (SGA: "The Storm", "The Eye")
After discovering an abandoned Wraith laboratory, the First Atlantis Reconnaissance Team manages to pull a data storage device from a computer console. Examining it, they find that the Wraith language is a derivative of Ancient, confirming the hypothesis that the Wraith evolved after the Ancients came to the Pegasus galaxy. Doctor Elizabeth Weir is able to translate the data and learns about the Wraith scientist's experiments that created the Wraithkin. (SGA: "The Gift")
When Ford's Coalition captures Lt. Colonel John Sheppard and his team, they reveal that they have managed to get at least one data storage device. The device contains data on a hive ship that is preparing to cull a human world, data that the coalition intends to use to destroy the hive ship first. (SGA: "The Lost Boys")