Beam forming is a vast concept but i try to explain logical part of it -
Beam-forming is massive(multi)antenna technology, which dissipate the power in certain direction(& angle).
In non - technical words - lightening CFL in a room will dissipate the energy in surrounding direction but lightening beamed torch will dissipate the energy in particular direction.
Advantage in wireless system - The biggest advantage(but not only) is - improved SNR. It sense, end users distance, direction, movement speed, traffic type etc and dissipate the energy in particular direction.