Most fans of mystery novels know a lot about detectives---likely more than they know about suspects and murderers. After all, the reader is usually following the case and evaluating the clues through the detective's eyes. The detective's mission to solve the case provides the spinal column of the mystery plot.
The path that journey takes, and the difficulties facing each sleuth is a large part of what distinguishes one mystery from another.
Many detectives feel a great deal of pressure: It's their haste to solve the case and prevent more deaths that drives the detective. They're trying to piece together clues and stop the murderer before he kills again. This component adds a sense of urgency and suspense to your book.
Some detectives experience the fear associated with a close brush with death. Perhaps they're getting too close to the truth and face possible elimination by a killer desperate to remain anonymous. This fear can either drive them or cloud their judgment.
Some detectives' personal foibles create drama. Police procedurals may showcase detectives dealing with grief, divorce, and substance abuse (usually alcohol) problems. Their focus may be diverted by their personal issues, or may lead to a slower resolution of the case. Some killers exploit the detectives' faults, insecurities, or inadequacies for their gains (remember The Silence of the Lambs.)
Some sleuths have something to prove---the policeman looking for promotion or one who bears a chip on his shoulder for being passed over for one. The amateur sleuth may be trying to clear his own name in connection with the crime. The desire to prove something and the internal conflict of the detective can add fuel to your plot--maybe during the "sagging middle" of the book where it seems that the crime may never be solved, or when there may be an additional crime committed, despite the detective's best efforts.
Many detectives have a well-developed need for justice. They share a sense of outrage at these crimes against innocent victims and a desire to return the area to its previous civility. In some books, the detectives may even occasionally extend mercy to the killer--if they believe their crime was justified and, in some respects, just (the crimes were committed to exact revenge over long-ago transgressions.)
The detective is your reader's host through your novel. By understanding what makes him tick, you're providing the reader with a more interesting and insightful journey through your book.