From the 4th century, the Korean language used to be a right-to-left vertically written language using Han Chinese characters with Korean pronunciation. This writing system is known as hanja (한자, 漢字) or Sino Korean, and it still resembles traditional Chinese and kyūjitai as it never went through major reform over the centuries. Full adoption of hangul, the phonetic alphabet, took around 500 years, only gaining fully widespread usage in the 1990’s or 2000’s.
As hanja was something only the wealthy of society could afford to do, it’s usage in modern Korean language has taken on a more noble or elite feeling. Roughly 60% of words used in modern Korean have hanja roots and these carry more formal feelings than words without roots. You may see hanja in formal advertisements, such as financial investing or golf clubs, or in more traditional settings but has disappeared from most forms of media and everyday life. When words are combined together, usually words with hanja roots are combined with other words that contain hanja roots. Likewise, words that have no hanja, sometimes called pure Korean, are joined with other words which cannot be traced back to Chinese.
What Latin is to English is like what hanja is to Korean. Learning a bit of hanja is useful for seeing connections in similar words as well. As the Korean alphabet is phonetic, similar sounding words are spelled the same but have very different meanings, for example the 교 in 교통 (transport) and 교육 (education) look the same on the surface but their roots are very different. Knowing the 교 in 교육 is 敎 and that is the same root in 학교 (learn + education location = school), 대학교 (large + learn + education location = university), 교내 (learn + inside = inside a school), 교복 (learn + clothing = school uniform), and 교우회 (learn + friend + gathering = alumni association) helps learn similar words.
Several books which can assist in learning the Sino Korean, aka hanja, connections between words include Handbook of Korean Vocabulary: A Resource for Word Recognition and Comprehension by Miho Choo and William O’Grady, Your First Hanja Guide: Learn Essential Chinese Characters Used in the Korean Language by the website Talk To Me In Korean, and Root Korean: A Dictionary of Korean Root Words (Hanja) by Andrew Livera.