A marble is 1 piece of a set of clues to uncover the truth of a mystery, conspiracy, a web of lies or other the pre-written truths designed by the organisers.
The essence of a marble structure is to regard a game-location including the characters present as placeholders for clues. Like a marble in a closed bag of marbles are the clues hidden from view. Every encounter either with the environment like character(not player), objects, piece of scenography or even a view of the landscape that gives the player a clue on how to solve a prewritten puzzle or mystery. The trick is that a player would need a minimum number of clues before being able to realize the hidden truth.
(compared to fates that explains everything:) There are several different interpretations of the fateplay idea, but they usually involve an instruction that the player should be able to achieve easily, with the challenge being more about achieving it in an interesting an meaningful way. For example a character might be given the fate that "Before the second night of the larp, you shall challenge the king to a duel on the third morning. You will lose this duel." The duel is unavoidable, but the details of the challenge and the fighting leave plenty of space for dramatic improvisation.
Fates may be inter-connected into a "fateweb" where individual fates reveal their meaning as they are carried out. For example, the King in the above example might be fated to reveal his complicty in the murder of the previous King before the second day, thereby providing a motivation for the character fated to challenge him to a duel.
Marbles may be used to adopt whole narratives to larp - e.g. stories derived from mythology, theatre plays and the like. "Light-weight fates" may be used to give the players good ideas for what to do during the larp. There are also examples of larps where the first part of the larp is fated, and the fates are used to establish interesting conflicts, while the rest of the larp is open-ended.
History and further reading
Theory of marbles was probably "invented" in Norway. Some (old) texts on larphacking are gathered at: Larp Hacking Wiki