In a nutshell, it's about a working class woman Mrs Johnstone who has twins, Eddie and Mickey.
She can't afford to keep both, so gives Eddie away to a well-to-do family who can't have children and are happy to adopt, and keeps Mickey.
Despite the mother's attempts, the two boys meet first when they're 7, and, unaware that they are real brothers, decide to be blood brothers (hence the title) by cutting their hands and mixing the blood.
The boys grow up into very different young men: Eddie goes to university and has good prospects, Mickey isn't doing quite so well.
They get into a bitter feud over the same girl, and it ends with Mickey shooting Eddie before turning the gun on himself.
It's a straight play but there is also a very popular musical version.
HTH!