Wicca is a fertility-based religion founded in the 1950s by Gerald Gardner, supposedly based as much as possible on pre-Christian British traditions and ceremonial magic societies/orders. Exactly what defines a Wiccan depends on who you ask, but at least one rule is consistent: "Wiccan" is not a fancy word for "witch,"note and "Wicca" is not a catch-all term for any neo-pagan religion. Neither is it a term for someone who practices "whatever feels right," even if they take some of their practices and beliefs from Wicca. (That's called eclectic paganism - not that there's anything wrong with it; it's just not Wicca.) Note that the number of people who call themselves Wiccan but do not meet this definition (often because they do not belong to an initiatory tradition or do not follow all these beliefs) is much greater than those who do.
In general, there are two main types of Wicca. The first type is coven-based, where adherents gather together to practice their religion. The oldest form of Wicca, established by Gardner himself (hence known as Gardnerian Wicca) is coven-based and is an orthopraxic mystery religion. Orthopraxic means that correct practice is more important than correct belief (orthodoxy). Like all coven-based forms, its core practices are oath-bound and are not taught to cowans or outsiders. This means that you can't actually practice Gardnerian Wicca as you'll have no way of actually knowing what a good chunk of the vital practices and rituals actually are. While there are many books about Gardenarian Wicca, there are no books that actually contain these core practices or Mysteries; at best, the books contain "outer court" information comprising of some history and generic neo-pagan beliefs and practices. However, since the original "Gardnerian" Book of Shadows has been printed multiple times, including what were (formerly) the secret names of the Goddess and God, most Gardnerian and Alexandrian covens have since augmented the original material with additional, actually still secret stuff. Also, it should be noted that because some of the rituals are sexual in nature (although a far cry from orgies), no one under the age of 18 is allowed to be initiated for legal and moral reasons.
Whilst Gardnerian Wicca was for some time the first and only form of Wicca, many other varieties have risen around it. One of the first of these, founded by first-degree Gardnerian initiate Alex Sanders, is Alexandrian Wicca, loosely based on its predecessor. Together with a handful of other coven-based forms tracing their heritage back into the New Forest region where Gardnerian Wicca sprang from, these sects comprise what is today known as "British Traditional Wicca", or BTW. However, many other "denominations" of coven-based Wicca have arisen since the evolution of BTW.
The other type is solitary, which is almost the exact opposite of coven-based forms. Firstly, practitioners are given more leniency in their beliefs and practice. Whilst the core tenets of Wicca are there (e.g. belief in the God and Goddess, the Wheel of the Year, the 3-fold law & Rede, etc.), solitaries may also hold different opinions regarding various topics, such as with adherence to different theories of magic. Solitaries also differ from coven-based Wiccans in that they freely share religious information, their primary sources being: the wide variety of books published regarding Wicca and similar metaphysical subjects, such as Buckland's complete guide to witchcraft, and ideas inspired by their own meditations, known as Unverified Personal Gnosis (UPG). Because of the accessibility of materials and a much greater number of outlets for solitaries, it is this face of Wicca that is the most familiar to non-Wiccans.
Exactly who has the right to call themselves a Wiccan has been debated. Some argue that Wicca without the Mysteries isn't truly Wicca, the same as Catholicism without baptism and communion wouldn't be Catholicism. This isn't to say that the path isn't valid and that the person doesn't have the right to practice and believe what they feel is right, but simply that calling their practice and beliefs "Wicca" would be superficial and meaningless. Others argue that the term can be applied to any path derived from Gardnerian Wicca, Mysteries or no. However, most Wiccans and Pagans (Druids and such) separate Gardenarian\Alexandrian Wicca from other types and consider them all valid.
Aside from this, Wicca is often misunderstood by other religions and Hollywood, and there are many unfortunate misconceptions. Wiccans do not worship the devil (the character simply doesn't exist in their theology), nor does their pentacle symbolize the devil. And before you ask, they typically consider spells to make specific people fall in love with you unethical, as it interferes with free will. Most do not go around cursing people, as they believe in the "three-fold law," which states that any action you do, good or bad, will return to you thrice over.
Whilst magic is a central theme of Wicca it is nothing like what you see in Hollywood or role-playing games but works in a manner more analogous to prayer (in fact, in Wicca, magic is most simply defined as "focused prayer"). Wiccans do not try to cast fireballs, nor do they fly on brooms, nor otherwise attempt impossible magical feats as you see in Harry Potter. Also, Wiccans do not sacrifice humans or animals (much less eat babies), nor do they proselytize. They are not on a mission to destroy or undermine Christianity (let alone lure Christians into a front group for Satanic worship). They are typically content to let Christians be as long as Christians let them be.
Wiccans worship the "God and Goddess of the [British] Isles," also referred to as the Lord and the Lady. Different covens have their own names for the Lord and Lady, but these are not revealed to cowans (solitaries also sometimes choose their own names to recognize the Lord and Lady by). They use the pentagram/pentacle to symbolize the five elements - air, earth, fire, water, and spirit. Others, even within traditions, may worship a personal patron (sometimes more than one), which may be chosen from the Norse, Greek, or other pantheons, in addition to the Celtic, and may incorporate other practices (such as Shamanism and Reiki) which are of non-Celtic origin.
Males who practice magic are simply called witches. The term "warlock" is said to refer to those who break the sacred oaths taken during initiation and divulge the Mysteries to non-Wiccans, and the actual etymology of the term 'warlock' indeed derives from "oathbreaker" in Old English. It is also quite offensive to call one such. The terms "wizard" and sorcerer/sorceress (and similar) are seldom used.
Wicca became "mainstream" to an extent during the nineties. The polemic writings of Silver Ravenwolf became popular, movies such as The Craft was released during this period, TV shows such as Charmed and Buffy the Vampire Slayer featured Wiccan characters, and the Harry Potter books, while not about real-life witchcraft in any way, inspired a few young people to take up witchcraft. Such portrayals were almost always inaccurate, sometimes confusing Wicca with either Satanism, other varieties of Neopaganism, or straight-up wizardry.
This page has some more in-depth information on the beliefs and origins of Wicca. Also, there are many, many myths and misconceptions about Wicca that would take forever to put up here, but are dealt with here, here, and here.