There are several holidays and observances on October 9, but the answer to the question depends on the context. If you are in the United States, October 9 is a federal holiday, and government offices, DMV, libraries, and courts are closed. The U.S. Postal Service is also closed, and there is no regular mail delivery. Some businesses may also be closed, but others may remain open. The holiday is inconsistently celebrated, meaning its a day off with pay at some businesses but just another start to the workweek at others.
If you are looking for specific holidays and observances on October 9, there are many listed on various websites. For example, October 9 is Indigenous Peoples Day, National C60 Day, National Digitool Day, National Pro-Life Cupcake Day, and World Post Day. It is also Columbus Day, Curious Events Day, Fire Prevention Day, Hangul Day, Independence of Guayaquil, Leif Erikson Day, and Day of the Valencian Community.