Interceptor is a name given to certain types of fighter aircraft whose major mission is destruction of strategic bombers. As is often the case, what exacty constitues an inteceptor, as opposed to an air superiority fighter is a matter of degree.
During World War II, the difference between ground attack, dogfighting and anti-bomber planes was not well defined. A P-51, for example, could fulfill all three roles well. However, with the advent of the cold war, changes in strategy and technology transformed the general purpose fighter into two categories: the tactical, and the strategic.
In the 1950's, the main object of United States foreign policy was to protect Western Europe from a Soviet attack. However, there was no possible way that the United States and NATO forces could handle a conventional war in Europe, so the United States instead depended on a trip wire strategy of massive strategic nuclear strikes against the Warsaw Pact at the first instance of conventional aggression against Western Europe. For this reason, conventional fighter-bombers and air superiority craft were not developed fully, since their mission would be futile anyway. What were developed, however, were aircraft meant to defeat a retalitory second strike (or possibly a first strike) of Russian bombers against the United States. For this reason, the United States Air Force ordered planes such as the F-101 Voodoo, F-102 Delta Dagger, F-106 Delta Dart for the purpose of downing Soviet Bombers. These planes were armed with nuclear tipped rockets and early guided missiles, as well as sophisticated (for the time) radar and computer systems. These planes, far from the machine gun armed dogfighters of World War II, could engage an enemy with missiles at far distances and without visual identification.
However, from the 1960's and onwards, the United States has not developed any planes purely for the use of strategic interception. The reasons for this are based in a change in nuclear strategy, and a geopolitical situation where the United States does not see itself facing any enemies equiped with strategic bombers. On the other hand, the Soviet Union only begin building interceptor aircraft, such as the MiG-25 Foxbat, and its succesor, the MiG-31 Foxhound, after the United States had stopped. Since I don't know the strategic thinking of the Soviet Union or Russia, I don't know why this is.
However, in the United States, the primary reason for giving up interceptor aircraft was based on the understanding that their mission was futile: that there would be no real way to stop the entire triad of Soviet bombers, missiles and submarines, and that the only real strategy was one of Mutually Assured Destruction, where each side would know that there would be enough nuclear weapons left after a first strike that the attacking side would be destroyed as well. The second reason for the reemergence of the fighter-bomber and air superiority fighter was the Vietnam War, which saw the United States Military fighting in a situation where the enemy didn't have an air force, and where smaller, more manueverable fighters that could double as ground attack aircraft would be more important. After Vietnam, although the United States has engaged in a number of wars, only one (The Gulf War) has been with an enemy with an appreciable airforce, and even that airforce didn't include any heavy bombers.
For that reason, every aircraft since Vietnam developed in the United States has been an air superiority fighter (F-4 Phanton, F-16 Falcon, F-20 Tigershark or a fighter-bomber (F-111A Aardvark, F-15 Eagle, F\A-18 Hornet, F-22 Raptor). A small exception may be the F-14 Tomcat, whose main role was to intercept fleets of cruise missiles aimed at carrier battle groups with the long range AIM-54 Phoenix. However, the F-14 can also be used as an air superiority fighter, and as a fighter-bomber.
For these reasons, the role of interceptor is currently not an important one in the United States Air Force, or in any other airforce in the world, for that matter.