Deadly force is that level of force which is inherently likely to cause death or great bodily injury. Firearms, blades and explosives are among those weapons the use of which is considered deadly force.
"Use of deadly force" is often granted to police forces when the person or persons in question is/are believed to be an immediate danger to people around him. For example, an armed man in a shopping mall shooting at random without regard to the safety of the people around him, and is refusing or is unwilling to negotiate, would likely warrant usage of deadly force, as a means to prevent further danger to the community.
In general, all armed bodies, be it the police or military or some offshoot thereof, have the ability to issue authorization for the usage of such force. Self-defence resulting in usage of deadly force by a civilian or civilians against an individual or individuals is often subject to examination by a court if it is unclear whether it was necessary at the point of the offence, and whether any further action on the part of the law needs to be taken.
See also: Police, non-lethal force.