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The word derives from the Latin for "hidden" or "secret" (occultus), and there is the suggestion that the occult involves "knowledge" known only to those with special training or powers.
While many of the early scientists, such as Isaac Newton, were also occultists, in modern times it is usually considered a pseudoscience. Notable 20th century occultists include Aleister Crowley, Gerald Gardner, and Anton LaVey. Some people really believe the kooky ideas, while others take them as entertainment. Whichever, they usually end up lighter in the pocket.
An example would be paying a "psychic" (or medium) to talk to dead relatives. This is pretty silly as it puts you under the influence of charlatans and confidence tricksters. To inquire about one's future success at work or in love, it can be amusing, and no worse than cheap therapy. However, far too many make life decisions based on the garbled obfuscations of people whose only motive is to line their pockets.
People seem to have a tremendous desire and ability to believe in the silliest things — watching the cast and guests of any episode of Ghost Hunters is evidence of this. To the skeptic, the only reason to watch is to play the "lowest IQ in this segment" competition. They are convinced that places are haunted, and desperate to have their superstitious ideas confirmed by plumbers with a bunch of gear from
Circuit City Best Buy.
Other people, again straddling the entertainment/belief lines, are into casting spells and incantations. This can be as fun and harmless as putting on a play, or as ludicrous as thinking the act has real-world meaning.
Most religions have an aspect of the occult, some more than others. They suggest or require belief in things without evidence or plausible mechanisms.
Western occultism has mostly stuck to the Hermeticist tradition of thought that sprang up towards the end of the Roman Empire. This school of thought was a major aspect of intellectual life in Europe all the way up to Newton, though after him it basically took a nosedive into the realm of crackpots and attention-seekers.
At its worst it amounts to a staggering failure to recognize that the map is not the territory, and to assume that anything that looks pretty or sounds good and manages to weave together a bunch of different religious traditions must be true. The result tends to be people who argue with a straight face about how the chakras relate to the Kabbalah, which is itself the underlying metaphor of tarot cards, as well as a sort of applied astrology, despite the fact that it is flamingly obvious to anyone with a passing knowledge of history that there is no remotely sane way for these ideas to be historically linked.
At its best, however, its central defect — an inability to distinguish between an interesting metaphor and an actual description of reality — turns into an advantage. This generally happens when occultists put down their magic wands and get around to making works of art — Algernon Blackwood, Arthur Machen, Alan Moore, Grant Morrison, Neal Stephenson, Bram Stoker, Dennis Wheatley, and William Butler Yeats, for instance, have all written works in which the Hermetic tradition is a major element, or have been openly involved in occultism at some point during their lives.
Thankfully, if you are actually arguing with an adherent of occultism, you can probably safely assume they are of the former category instead of the latter, but if you inadvertently pick a fight with a member of the latter category, you may quickly find yourself getting slapped around for being way, way out of your actual areas of expertise.