They are called the White Walkers or the Others. They lived in the northern edge of the world (The Land of Always Winter) and perform rituals unknown and other things not yet known even in the books. Little is known about them, but they were driven off 8,000 years ago after fighting with the alliance of the First Men and Children of the Forest - it lasted for a whole generation and was called The Long Night. They are believed to be just myths as of now, but after magic made a reappearance in the world, so have they. Any person or animal they kill will be reborn as a Wight (or zombie if you wish). The White Walkers can be killed with dragonglass (Sam used a dragonglass blade to stab, hence he died). Wights can't be killed by dragonglass though, they can only be killed by fire. It is not known whether the Others can be killed by fire too, but they don't like it very much and stay away from it and light.
And regarding the baby, it is not known why he was after it. Craster was giving away the babies to them till now and they kept away from him; but now he's dead and the supply has stopped. Perhaps they raise them as their own, or perhaps they're building an army for comeback? Or maybe they sacrifice them for some unknown blood magic ritual? This is one topic where Irri and Jhiqui cannot say "It is known".
