Twinsen's ID Card is just a card that Twinsen can use to identify himself. It has Twinsen's ID number (0731) and a photo of him, along with FunFrock's symbol. The card was taken from he when he was imprisoned before the start of his adventure, when he wakes up in his cell.
Twinsen can get the card that was taken from him in a room in the citadel, along with his holomap. Although he can show his ID card to several citizens and guards, it is usually not adviceable to do so, as people often recognize him from the "wanted" posters as an escapee.
"Twinsen's ID Card. This card allows you to identify yourself to the authorities. Your smile is especially attractive on the photo!"