Someone trying to answer this question might end up talking about the sound of one hand clapping, fingers pointing at the moon, emptiness, and other mind-boggling things.
Zen is transmitted outside of words, direct from the mind of the teacher to the mind of the student.
The word "Zen" is Japanese for a style of Buddhism, but didn't Buddhism come from India?
Let's start from the beginning.
Buddhism is a religion based around the teachings of the Buddha, or the Awakened One, who lived around 500 years before Christ. He taught that in life, suffering or dissatisfaction is inevitable. Suffering has causes, those causes can be cut off, and there is a way of life that will allow someone to do this. These are called the Four Noble Truths, and the way of life is the Eightfold Path: Right Views, Right Intention, Right Speech, Right Attitude, Right Livelihood, Right Effort, Right Mindfulness, and Right Concentration. Following the Eightfold Path, he taught, will lead to Nirvana, the "putting out of fires," and suffering will end.
In order to live in such a way, many Buddhists emphasize the value of meditation. In the ancient Indian language Sanskrit, "deep meditation" is dhyana (ध्यान).
When Buddhism arrived in China, the Chinese had to find a way to talk about these new ideas for which there were no Chinese words, so they imported the words along with the ideas. Just as foreign words like "karaoke" and "typhoon" entered the English language, dhyana entered the Chinese language. As Chinese has different sounds than Sanskrit, they pronounced the word "chan-na." They used two Chinese characters to write the word by sound, without regard to the characters' meanings, something like drawing a car and a pet dog to write "carpet."
Later, in the 5th century, an Indian monk named Bodhidharma came to China. Bodhidharma stressed meditation so much that he supposedly cut off his eyelids to keep from falling asleep when meditating! His style of Buddhism came to be known as the Meditation School, or "Chan" for short.
Many Chinese intellectuals, poets, and artists were attracted to Chan's simplicity and spontaneity, perhaps because it reminded them of their own Taoist tradition. Chan became a great influence in Chinese culture.
Since China was the dominant nation of the day, many of its neighbors borrowed and learned from it. Many Japanese went to study in China, and eventually, Chan Buddhism was brought to Japan by a monk named Eisai in the 13th century. The Japanese, who had already imported Chinese characters into their own language, learned the character for "Chan" and pronounced it "Zen."
Zen became very influential in Japan, perhaps even more influential than it had been in China. In fact, it became so well-known that many people in the West think of it as a Japanese concept. Just as the Japanese borrowed the word from the Chinese, who borrowed it from the Indians, we have borrowed it from the Japanese, and now Zen is an English word.
Now the real question -- What is "Zen"?
This question basically asks "What is the essence of Zen?" It appears in various guises throughout Zen literature, from "What is the meaning of Bodhidharma's coming from the West?" to "Have you eaten yet?" The question cuts right to the heart of the matter and can only be answered by you.
Perhaps the best answer is "practice".
That is the meaning of the word "Zen." As for the idea itself, well, you’ll have to meditate on it:
I can’t tell you or it wouldn’t be Zen.
Why does Zen sometimes seem like nonsense?
One of the central points of Zen is intuitive understanding. As a result, words and sentences have no fixed meaning, and logic is often irrelevant. Words have meaning only in relation to who is using them, who they are talking to, and what situation they are used in. Zen and poetry have gone hand in hand for centuries.