Shalom Paul,

The basic sources that discuss the Goel ha'Dam are Bamidbar 35, Devarim 19, Gemara Makos Dapim 10-12, and Rambam's Hilchos Rotze'ach u'Shemiras Nefesh. So that is where I recommend further reading. But, generally speaking, he is the relative who inherits the estate of someone who was killed. His role is to avenge the death of that murder victim. As such, he is entitled to kill the perpetrator (or, according to one opinion in Makos, he merely is exempt from punishment if he does so), except when the latter is safe inside the boundaries of a city of refuge. There are many associated details, such as if victim was killed by accident, then the killer is released from exile when the Kohen Gadol passes away, and after that point the Goel ha'Dam may no longer harm him.

Please let me know if you'd like me to provide or analyze additional passages.

Wishing you a Chag Kasher v'Sameach!

Yishai Rasowsky