Hangul Jamo, the alphabet used to write the Korean language, consists of 24 letters -- 14 consonant letters and 10 vowel letters. Historically, It had 28 letters, with 3 more consonant letters and 1 more vowel letters, but for these sounds are not present in modern Korean, they are no more used.
Hangul was invented by the 4th king of Chosun Dynasty, King Sejong, and his researchers. The system was completed in 1443, and published in 1446. October 9th, the date of publication of Hangul, is a national holiday in Korea.
While the language looks ideographic to some Westerners it is actually phonetic. Each Hangul syllable is consists of individual letters (Jamo) connected in any of three patterns. Syllables that end in a vowel are written either vertically or horizontally, depending on the vowel. Syllables which have a "vertical" vowel and end in a consonant are written clockwise, with the consonant at the bottom. Syllables which have a "horizontal" vowel and end in a consonant are written in vertical stack, also with the consonant at the bottom. The result is the same size and shape as a Chinese character.
Indeed, Hangul was generally used along with Chinese characters in most Korean writing until the late 20th century. Chinese characters are still used for personal names and in some newspaper headlines and book titles.
The designs of individual Hangul consonant letters model the physical morphology of the tongue, palate, teeth and throat. Vowel letters, on the other hand, consist of three elements. Horizontal line (which signifies the Earth), point (the Heaven) and vertical line (the Human).
There is a widespread rumor that claims that King Sejong visualized the written characters after studying the intricate lattice. But this is simply not true. Hunminjeongeum -- the publication of Hangul writing system in 1446 -- explains principles of letter designs, as you see above.
See also Korean language.