Shan't is a contracted form of 'shall not' used mainly in British English. It denotes negation of future intention or obligation and is more formal or traditional in tone. In casual speech it can sound antiquated or ironic; in careful speech it's clear and crisp, with a strong contraction that links the auxiliary to the negator. The pronunciation typically reduces the vowel in 'shall' and merges with 'not' when spoken quickly.
Full pronunciation guide