It is used to add a narrow space, such as between nested quotation marks or to separate glyphs that interfere with one another.
It is also used in the International System of Units and in many countries as a thousands separator when writing numbers in groups of three digits, in order to facilitate reading.
Some text editors, such as IntelliJ IDEA and Android Studio, will display the character as its suggested abbreviation of "THSP".
In LibreOffice's Symbol dialog, there is an easy-to-find box field to narrow the searching; in Word's Symbol dialog, under font = "(normal text)", the characters are found in subset = "General Punctuation", Unicode character 2009 and nearby.
Other word processing programs and in many Linux configurations, have ways of producing a thin space using keyboard shortcuts.