Montag remembers the memory of trying to fill a sieve with sand because it was a hopeless task, just as memorizing the books seems to be.
A sieve is a bowl with tiny holes. It is used to sort larger sediment from smaller, less valuable pieces.
Montag has become disenchanted with his society. He used to enjoy his job as a fireman, burning books. Now he sympathizes with the book-hiders and is actually joining them. He stole a Bible from a woman who decided to die with her books, and is desperately trying to memorize it to save it. As he tries to memorize the book, he remembers how he felt when he tried to fill a sieve with sand.
Once as a child he had sat upon a yellow dune by the sea in the middle of the blue and hot summer day, trying to fill a sieve with sand, because some cruel cousin had said, "Fill this sieve and you'll get a dime!" (Part 2)
Part II is called “The Sieve and the Sand” because Montag’s attempt to understand society and fit into it has become hopeless. It is not exactly that Montag considers Faber and his friends as cruelly tricking him in the memorizing of books, as the cousin did with the sand. Instead, Montag feels hopeless because all he knew is gone. He feels lost and confused. As much as he wants to save the books, he is not sure he is up to the task.