The British overseas citizen (BOC) status arose as a result of the independence day arrangements of former British territories (mainly former British colonies) and how nationality was granted in the newly independent country with regards to, amongst other things, where the parents were born.
Those eligible to apply for a British passport describing themselves as a BOC may gain advantages in applying for visas for other countries and are entitled to the protection of the British government in times of need overseas.
It is possible, in some circumstances, to upgrade a BOC to full British citizenship. This is sometimes possible even if another nationality is held. This is a complex area of British nationality law and requires specialist advice.