The Twitter app has gone through many transformations over the years, some of which were never rolled out widely. The company has just announced one test you might have been a part of is going live for everyone—the new Explore tab. No more will you have separate areas for search, Moments, and trends. They're all together in Explore.
Explore will take over for the Moments tab in the main app interface. It has a magnifying glass icon, and some of you may have already seen this in the app without realizing what was up. Twitter says this feature is rolling out to Android over the coming weeks, but at least some people on the AP team have had it for a week or two already.
When you open Explore, there's a search box at the top with trends right below that. Moments are down at the bottom; it seems like Twitter is de-emphasizing this feature a little. See above for a comparison between the old Moments tab and the new Explore tab.
It doesn't matter if you've got the stable, beta, or alpha version of Twitter. You'll get the Explore tab whenever you get it.