The term "hermetic magic" is used in several role-playing games, such as Ars Magica and Shadowrun. In both, hermetic magic is used to refer to an essentially scientific approach to magic -- which views the world as a collection of impersonal energies which can be harnessed by the use of special knowledge. In real history, the term "hermetic" comes from the writings ascribed to Hermes Trismegistus, which were logical in tone but also steeped in mystical assumptions and religious implications.
The Hermetic writings, or "Hermetica", were probably written between the middle of the 1st and the end of the 3rd century AD. However, they were essentially unknown in Western Europe until they were translated from Greek into Latin by Marsilio Ficino around 1463.  The texts were originally attributed as being ancient pre-Christian texts, thus the coherence of them with Christian theology was seen as being remarkable and proof of the universality of its ideas. The writer of the works is referred to as Hermes Trismegistus ("Hermes the Thrice-Great"), and was associated with the Egyptian god Thoth as well as the Greek Hermes.
Hermetism does suggest that true knowledge can be acquired through observation of the material world, but it was not at all "scientific" in the modern sense of the term. The aim of Hermetism, like that of Gnosticism (a contemporary religious-philosophical movement), was the deification or rebirth of man through the knowledge (gnosis) of the one transcendent God, the world, and men. This was important, however, in that other philosophical traditions often simply did not value empirical observations.
In Hermetic magic, the deification of man is seen as a practical task, which can be approached through astrology, alchemy, and other occult sciences. There are few actual details of magic in the original Hermetic texts themselves, but the European Hermetic tradition was certainly rife with magical practices.  The actual practices and beliefs varied widely. However, that is beyond the scope of the short definition I am providing here.
An important point to note was that the Hermetic magic was generally viewed by its early practitioners as being compatible and indeed an integral part of Christian beliefs.  Its aim was bringing the soul of the magician closer to God. The Hermetic texts themselves have vaguely Christian references such as "Father" for the supreme deity and "Son of God". This was probably the most important part of Hermetism, in that it lent a religious legitimacy and philosophical dignity to what were often viewed as corrupt activities.