how important is it for a cop to give you your miranda rights

Before a suspect in police custody (which doesn't necessarily mean under arrest) can be questioned by the police or any government agent, he or she must be given what is known as a "Miranda Warning", i.e. informed of certain rights they have (to counsel, to remain silent, etc.)  If the suspect is questioned without having been "read his rights", any evidence derived from that illegal questioning will not be allowed as evidence against the suspect at his or her trial (with rare exceptions).  This includes evidence which didn't come directly from the questioning, but was "fruit of the poisonous tree", for example if the un-mirandized suspect tells the police where he disposed of the murder weapon, and the police wouldn't have found it except for the illegal questioning, the gun will not be allowed in evidence at that suspect's trial, although it might still be admissible, under certain circumstances, against another person whom the police didn't question illegally, like an accomplice.