These two characters don't combine to create a literal meaning. Instead, this is a phonetic loanword (音译词, yīnyìcí). The characters were chosen because their pronunciation, jiā + kè, sounds very similar to the English word “jacket.” This is a common way modern words for foreign objects are created in Chinese.
The existence of the word 夹克 (jiākè) itself is culturally significant. Unlike traditional Chinese garments which have native names like a `旗袍 (qípáo)` or `唐装 (tángzhuāng)`, 夹克 is a relatively new word that reflects the influx of Western culture and fashion into China during the 20th century. The adoption of the jacket, and its name, went hand-in-hand with the adoption of Western styles. The leather jacket, 皮夹克 (pí jiākè), for example, carried the same cultural symbolism of “coolness,” rebellion, and rugged individualism in China as it did in the West, popularized through movies and music. This contrasts sharply with traditional Chinese outerwear like the `马褂 (mǎguà)`, a type of short jacket worn by men over a long robe. While the `马褂` represented a connection to tradition and a specific social status, the 夹克 represents modernity, globalism, and a break from that past. The simple use of this loanword tells a story of cultural exchange and China's integration into the global community.
夹克 (jiākè) is a common, everyday word used in a variety of modern contexts. It's considered neutral in formality.
It's often combined with other words to specify the type of jacket:
The most common point of confusion for learners is distinguishing 夹克 (jiākè) from other general terms for outerwear.