Okay, to answer this question, let's break it into two questions: What is a detective, and what is homicide?
A detective, also known as an investigator, is a police officer whose job is to investigate crimes. They often interview witnesses and suspect(s) in order to solve a case (crime).
Homicide is defined as the taking of one life by a member of the same species (homo= same, -cide = to kill). A homicide ranges from one of two justifiable offenses (self-defense or accident), to one of several degrees of criminal homicide, which severity of offense ranges from manslaughter by culpable negligence to capital murder.
So a homicide detective, or homicide investigator, in short, is a police officer who is a member of the Homicide division of a law-enforcement agency, and accordingly, whose job is to investigate homicide cases.