First, let's correct something: The Japanese romanization for this character, “Zen” has penetrated the English language. In English, it's almost always incorrectly used for phrases like “That's so zen.” Nobody says, “That's so meditation” - right? As the title of a sect, this would be like saying, “That's so Baptist!"

禪 by itself just means “meditation.” In that context, it should not be confined to use by any one religion or sect.

Regardless of the dictionary definition, more often than not, this character is associated with Buddhism. And here is one of the main reasons:
Zen is used as the title of a branch of Mahayana Buddhism, which strongly emphasizes meditation practice.
However, it should be noted that Buddhism came from India, and “Chan Buddhism” evolved and developed in medieval China. The Chinese character “Chan” was eventually pronounced as “Zen” in Japanese. Chan Buddhists in China have much in common with Zen Buddhists in Japan.

More about the history of Zen Buddhism here.

Please also note that the Japanese Kanji character for Zen has evolved a little in Japan, and the two boxes (kou) that you see at the top of the right side of the character have been replaced by three dots with tails. The original character would still be generally understood and recognized in Japanese (it's considered an ancient version in Japan) but if you want the specifically modern Japanese version, please click on the zen Kanji to the right. Technically, there is no difference between the Tensho and Reisho versions of Zen since they are ancient character styles that existed long before Japan had a written language.

There is also an alternate/shorthand/simplified Chinese version, which has two dots or tails above the right-side radical. This version is also popular for calligraphy in China. If you want this version, just click the character to the right.

Further notes: Zen is just one of seven sects of Buddhism practiced in Japan. The others are 律 Ritsu (or Risshū), 法相 Hossō, 論 Sanron 華嚴 Kegon, 天台 Tendai, and 眞言 Shingon.

見性成佛 is a universal phrase that suggests that one may see one's nature and accomplish Buddhahood.

見性 suggests penetrating deep inside oneself to see one's “Original finally Mind.”

成佛 refers to a sentient being who dispenses with illusions and delusions through ascetic practice, is enlightened to the truth, and becomes a Buddha.

This is used by Mahayana, Chan, and Zen Buddhists in China, Korea, and Japan.

You will also see this with the last character written as 仏 in Japanese. In the religious context, 佛 is commonly used to mean Buddha. If you want the other version, see Kenshō Jōbutsu 見性成仏

This encompasses the idea of meditation.

It's also a term used to describe a deep form of daydreaming, exploring one's imagination, the act of contemplating, or the idea of contemplation. 冥想 is often associated with Buddhism; however, the word “Zen” in Japanese (or “Chan” in Chinese) is probably more commonly used (or better known in the west).

See Also:  Zen

禪宗 is one way to title “Zen Buddhism.” Because the original pronunciation of Zen in Chinese is Chan, you'll also see this expressed as Chan Buddhism.

From the Buddhist Dictionary:
The Chan, meditative or intuitional, sect is usually said to have been established in China by Bodhidharma, the twenty-eighth patriarch, who brought the tradition of the Buddha-mind from India. This sect, believing in direct enlightenment, disregarded ritual and sūtras and depended upon the inner light and personal influence for the propagation of its tenets, founding itself on the esoteric tradition supposed to have been imparted to Kāśyapa by the Buddha, who indicated his meaning by plucking a flower without further explanation. Kāśyapa smiled in apprehension and is supposed to have passed on this mystic method to the patriarchs. The successor of Bodhidharma was 慧可 Huike, and he was succeeded by 僧璨 Sengcan, 道信 Daoxin, 弘忍 Hongren, 慧能 Huineng, and 神秀 Shenxiu, the sect dividing under the two latter into the southern and northern schools: the southern school became prominent, producing 南嶽 Nanyue and 靑原 Qingyuan, the former succeeded by 馬祖 Mazu, the latter by 石頭 Shitou. From Mazu's school arose the five later schools.

In Japanese, 無心 means innocent or without knowledge of good and evil. It literally means “without mind.”

無心 is one of the five spirits of the warrior (budo) and is often used as a Japanese martial arts tenet. Under that context, places such as the Budo Dojo define it this way: “No mind, a mind without ego. A mind like a mirror which reflects and dos not judge.” The original term was “mushin no shin,” meaning “mind of no mind.” It is a state of mind without fear, anger, or anxiety. Mushin is often described by the phrase “Mizu no Kokoro,” which means “mind like water.” The phrase is a metaphor describing the pond that clearly reflects its surroundings when calm but whose images are obscured once a pebble is dropped into its waters.

This has a good meaning in conjunction with Chan / Zen Buddhism in Japan. However, out of that context, it means mindlessness or absent-mindedness. To non-Buddhists in China, this is associated with doing something without thinking.
In Korean, this usually means indifference.

Use caution and know your audience before ordering this selection.

More info: Wikipedia: Mushin

八風吹不動 is an ancient Buddhist phrase from about 1000 years ago.

Literal meaning: “The Eight Winds cannot move [me].”

The original famous anecdote is from Song Dynasty China, involving the poet-official 蘇東坡 (Su Dongpo / Su Shi, 1037–1101) and Zen master 佛印 (Foyin).

Su Dongpo wrote 八風吹不動，一屁打過江
“The Eight Winds cannot move me; Yet one fart blows me across the river.”

Foyin’s irreverent reply exposed Su Dongpo’s ego, which is kind of a classic Zen/Chan teaching story.

There is a shorter Japanese Zen version, 八風不動, which drops the middle character. Often romanized as happū fudō. The romanization of 八風吹不動 is arguably happū fukedomo ugokazu or happū sui fudō.