What is phantom stock/virtual shares?

Phantom stocks or virtual shares provide for the same economic benefits to the employees as regular shares would. The reason why no regular shares are distributed are multiple, one being that it is much easier to sign an agreement with employees for certain benefits linked to the development of the company than it is to issues shares, transfer shares (for a German GmbH, the transfer would require notarization) and potential redeem shares upon cancellation of employment.
In terms of taxation, there may actually be a benefit to transfer real shares as all profits from the increase in value of the shares once they have been transferred to the employee (the capital gain) are taxed at a lower rate that employment income is. Virtual shares do not provide for that possibility.