A phrase, usually used to be crude, indicating the age by which a girl should be having sex. "Old enough to bleed" refers to the age a girl begins menstruation, usually around 12, but can be between 8 and 16 years of age. "Old enough to breed" means that when she mensrtruates she can have children, but of course she can not have children unless she has sexual intercourse.
Another way to rephrase this is "if she has started getting her period, she is old enough to have sex". Of course in many cultures, a girl is usually under the age of consent when she begins her period, so the result could be statuory rape. However, the female body begins menstruation earlier than the age of consent because years and years ago, humans did not live long, so it was necessary for the survival of the the species. For example, during the Roman Empire, the average life expectancy was 22 years.
Pheromones released during ovulation attract males to females who are able to bare children and cause them to become erect and desire intercourse with the ovulating female, so before civilization imposed restrictions on human sexuality, females would become sexually active when the began ovulating. While this is not a justification to have sex with underaged girls, it does explain why human females are able to have children long before society permits them to have sex.
At face value, the phrase states the obvious truth that once she begins menstruation, she can begin to have children, but as stated above, this is not how the phrases is commonly used.
Overheard at a junior high school party:
"I can't believe you went all the way with Sally, she's only 12!"
"Yeah, well, you know what they say... 'old enough to bleed, old enough to breed'. She was hot and horny too, you know."