Normal antennas emit electromagnetic radiation – you can think of it as being like the ripples a stone makes when it falls into water. The waves travel in every direction away from the source, forming a circle.
Beamforming is a technology that manipulates the radiation waves, steering and enhancing them in a desired direction – towards the user's mobile phone, for example. This is accomplished by emitting waves from several antennas in a way that multiple waves can add on to each other.
Several receivers or transmitters are set at a certain distance from one another, and by introducing delays to the transmitted electromagnetic waves, the receiver will receive added amounts of energy. The signal will therefore become stronger in a certain direction. Adaptive delay methods allow the movements of the transmitter and/or receiver to be adjusted, resulting in the electromagnetic radiation becoming stronger in one single direction – forming a beam. Hence the name Beamforming.
This technique is used to strengthen electromagnetic radiation and can actually work with any kind of wave, even sound or water. With antennas, this can be done in a digital or analogue way – either software does the beamforming in a digital form, or the antennas themselves can be built in a way to form a beam in a certain direction.
The digital variant is much more flexible and also allows for three-dimensional beamforming (3DBF), instead of just two-dimensional beamforming (2DBF). 3DBF is more advanced in that it works simultaneously in both horizontal and vertical environments (imagine a 3D environment like a city skyline). Whereas 2DBF works best in an environment that is only horizontal or vertical (imagine a flat rural area without the need to deliver a signal to devices located upwards).