The new search bar is located above the the DM interface in the Twitter app or on the web and it can be used to locate specific conversations and key words.
DM search first debuted in August, when Twitter said that it was testing out the feature. Some users have had the search bar since then as part of the test, but as of today, it's available for everyone.
Get your search on. DM search is rolling out to everyone on iOS today.— Twitter (@Twitter) October 1, 2019
Twitter can be downloaded from the App Store for free. [Direct Link]