In gambling, snake eyes is the outcome of rolling the dice in a game of craps and getting only one pip on each die. The pair of pips resembles a pair of eyes, which is appended to the term 'snake' because of the long-standing association of this word with treachery and betrayal. In modern parlance, it refers to such a roll in any game involving dice. Because this is the lowest possible roll, and will often be a loser in many dice games, the term has been employed in a more general usage as a reference to bad luck.
Coincidentally or not, the episodes in which Daniel wears the snake eyes shirt are always unfortunate. In Fleeing The Watcher, Bree and Daniel become so intimidated by the "watcher" outside their motel that they run away without even knowing where to go next. The Ends Justify The Means was an OpAphid video featuring hidden camera footage of Daniel in his bedroom. This video shows Daniel discovering the cameras that OpAphid was using to watch over him. Daniel later recounted that he had "freaked out" and left his house.
Fans associated Daniel's snake eye shirt with the premonition that his luck was running out. This connection appears to have been solidified by his wearing the notorious shirt in the video Miss Me?, which was filmed and released after he was kidnapped and brainwashed by OpAphid. Just as you can hardly get a worse dice roll than two ones, Daniel's bad luck was clearly at its peak when he was held by OpAphid.
The theme is continued in season 2, with Daniel wearing the snake eyes as he tells us that he wasn't accepted back into film class.