The cart pass is a black card with the worlds "Twinkle Circuit PASS" written on the front. Oppositely, the back is white with unreadable text.
In Sonic Adventure, and its enhanced port Sonic Adventure DX: Director's Cut, the cart pass is used by Knuckles, E-102 Gamma, and Tails to access the Twinkle Circuit mini game since these characters cannot access Twinkle Circuit during their regular storylines. As such, the cart pass is necessary to play Twinkle Circuit with the three characters, which is needed to collect all the Emblems.
The cart pass can be found on the triangle-shaped patch of grass in front of the hotel in the Central District after clearing Tails, Knuckles or Gamma's respective storyline.