A beam is one of the six metaphysical girders that support the Dark Tower at the center of existence. They are incredibly old and have been in existence since rising from the Prim.
The six beams cross like the spokes of a wheel, and are guarded at their ends by twelve Guardians. These twelve guardians are: hare, bear, horse, dog, eagle, elephant, rat, wolf, turtle, fish, bat and lion. Each guardian protects one end of the six beams. In centuries past, The Old Ones attempted to create their own versions of the beams and in so doing replace the guardians with cyborgs. But with passing of The Old Ones and the passage of time their technology began to deteriorate, which lead to the bear Shardik's destruction when Roland Deschain's ka-tet first started down the Beam of the Bear, the Way of the Turtle.
The beams themselves have been deteriorating for quite a while due to the machinations of the Crimson King. Using people, with a plethora of psychic abilities, called Breakers the Crimson King has brought down of the beams. By the end of the novels it is estimated that only two of the beams remain.
One of the first beams to fall was the Eagle-Lion beam which partially destroyed Roland's birth home, Gilead. The effects of a beamquake, when a beam is destroyed, are cataclysmic in proportion. What Roland and his ka-tet felt when one of the beams fell in the novel, Song of Susannah, was as simple as an earthquake, albeit a rather a strong one. But the closer you come to where the beam fell, the effects rise exponentially. Roland states at one point that if the beam had fallen within a hundred miles - maybe even a thousand - nothing would be left standing. The very birds would fall flaming from the sky. Also the effects of a beamquake are also felt extra-dimensionally. The only stated instance was felt as an earthquake.