The basic rule about searches incident to lawful arrest is that the arresting officer may, without a search warrant, search the person being arrested and the area within that person's immediate vicinity. The point of this exception to the requirement for a search warrant is to protect the police and to prevent the destruction of evidence.
The rule is meant to allow the police to search the area that an arrestee can reach. Police, it is ruled, should have the ability to search this area so that they can ensure that the suspect cannot obtain a weapon or something that might be used to escape custody. In addition, the rule is meant to allow the police to ensure that the arrestee cannot destroy any evidence that might be within his or her reach.