Why is it said that if we have a duplicate ciphertext block it can leak our information? I have been recently going through a question:
https://security.stackexchange.com/questions/15767/what-do-key-size-and-block-size-mean-in-cryptography and it created in me a series of doubts. Referring to the 2nd answer you may find the information that there is 50 percent chance of repetition of a duplicate block if we receive the square root of total amount of data. If some how a block is repeated how can it be cracked? How does the information gets leaked?
The exact information leaked depends on the mode of operation that is in use.
The simplest case is ECB, where a duplicate ciphertext block means that the corresponding plaintext blocks are also equal.

For the CBC mode, when two ciphertext block are equal, i.e. $C_i=C_j$, we know that there was equality before applying the block cipher. This in turn implies:$$C_{i-1}\oplus P_i=C_{j-1}\oplus P_j.$$
Equivalently, you are learning that $P_{i}\oplus P_j=C_{i-1}\oplus C_{j-1}$.

EDIT The equality comes from the fact that in CBC mode, $C_i=E_K(C_{i-1}\oplus P_i)$ where $E_K$ denotes the block cipher in use.