It is set in the current time, but with unusual elements such as animals who talk, flying cars, faeries, ghosts, and other non-indigenous creatures. It is set in our world, not a separate reality. Think of modern horror with lighter elements to it and a sense of wonder. Usually it starts with people having normal lives that are interrupted by the fantastical elements bursting in.
Although usually set in modern cities, technically any city will do, such as Victorian London or WWII Paris. The important part is that the city becomes one of the characters in a way—the setting is crucial. Usually there is a magical / horror layer—what comes out at night in a dark alley. Is that guy on the corner painted silver, or is he actual silver and drains the life out of children each night? Usually there is a strong romance going on between two of the main characters, although that is not the primary idea driving the plot.
Sometimes called “Sword & Sorcery”, it must take place in a time earlier than the 20th century, and often between 1100-1600 C.E. or in Ancient Greece. Culture has a major influence, whether it is trying to be accurate to a specific time period, or a sort of alternate history world. Most of the fantasy that first comes to mind, especially ancient faerie tales, falls into this category. Steampunk could be put under here as well, although it is different enough to warrant its own area and I would put it more with Science Fiction.
Filled with large numbers of characters and worlds on the brink of extinction if the intrepid hero cannot save them, high fantasy is concerned with the bigger picture and has a grand scale to it. Books such as Lord of the Rings come to mind. A Song of Ice and Fire is more difficult to place, because despite the threat from The Others, most characters are only interested in personal quests. I would personally put George R.R. Martin into this category simply from the scope of his works.
Alternate / Parallel Worlds
When a few modern characters find themselves pulled into secret kingdom of dwarves, it’s time to look at the alternate worlds sub-genre. I mostly use this because it is what faerie stories use—plain normal life of a cottage and the character is down on their luck, then they help an old woman across a stream and poof—into a magical castle with talking chalices. The Chronicles of Narnia is a famous example of the parallel world, and the popular Australian series Elephant Girl where a modern day girl discovers she is the mythical princess of an alternate realm. What is great about this genre is that there are characters we can relate to that ground the mythological elements, and can demonstrate the wonder of being in their first tournament. Knights in a historical fantasy would be more “whatever” about it. Popular plots include: Stranger in a strange land, Between the worlds, Multiverse, Alternate Timeline, Out of Phase.
Gloomy dread-filled Gothic tales of sweeping moors and abandoned mansions fill this sub-genre. It has a lot in common with other supernatural books, but tends to be more interested in the horror element as something to be explored. What are the creatures who go bump in the night thinking? Why do they have the lust to kill? Often the protagonist is not trustworthy and haunted by his or her own demons. If you get chills reading the book, it probably falls into this category.
Technically it is a sub-genre of romance novels, but it can overlap with fantasy, so I included it. The most common setting is modern times with otherworldly creatures falling in love with humans, or people who gain special abilities such as telekinesis. Occasionally the romance will happen between two supernatural beings, such as a wizard and a succubus, and sometimes they are set in the past or future. Usually it explores what happens as a normal modern protagonist falls in love with a creature from a secret world or different time. As of this moment, it is quite popular as a sub-genre.