The ts_headline function in PostgreSQL takes a text and a search query as input. It first parses the query into individual search terms. Then it searches the text for these terms. When it finds matches, it wraps those words with highlight tags, usually <b> tags, to emphasize them. Finally, it returns the text snippet with highlighted words. This helps users quickly see where their search terms appear in the text. For example, given the sentence 'The quick brown fox jumps over the lazy dog' and the query 'fox | dog', ts_headline highlights 'fox' and 'dog' in the output. The process involves parsing, searching, wrapping, and returning the highlighted snippet.