In general, this is the energy at a reference level. In classical thermodynamics, it is the energy at absolute zero temperature. All energy levels at higher temperatures are referenced to this.
There are some strange people on web sites that claim that this energy can be tapped. Others say that this energy is almost infinite and controls the rate that time passes. These people do not know about quantum mechanics that gives a very small value for this energy.
The zero point energy for a classical harmonic oscillator is 0. On the other hand, the ground state of a quantum oscillator is not zero. so why is this? in simple words, it is due to the uncertainty principle.
zero point energy does not mean that the energy is zero at all. According to the Second law of thermodynamic, all matters still possess certain amount of minimum energy when they approach to absolute zero i.e. - 273.16 degree celsius. As a matter of fact, it is impossible to achieve absolute zero. Therefore, don't be misled by the name of 'zero point energy'.