If thieves, hackers, law enforcement, or other would-be enemies should ever gain entry to your smartphone, they could also access conversations you've had in Signal Private Messenger. To better secure your encrypted communications, you can password-protect the whole app and its contents — but only on Android. Even then, it's necessary to perform data deletion on a periodic basis, if not immediately.
To delete a single message inside of a conversation with another person in Signal, just perform a long-press on the individual line of text then select either "Delete" (iOS) or the trash can icon (Android). To delete an entire conversation, from the main inbox screen, either swipe left and tap "Delete" (iOS) or long-press on the thread and tap on the trash can icon (Android).
Erasing single messages or entire threads right away is a good idea if there's highly sensitive information you want to keep away from unintended eyes. However, if you're not a whistleblower at the NSA or a hacker sharing cloned credit card numbers, you'll probably be just fine cleaning up messages on a periodic basis.
The easiest way to do that is to just delete all conversation threads you have going in Signal at the same time on a daily, weekly, or monthly basis. Bulk deleting conversations is slightly different on Android and iPhone, so hit up your respective section below to see how.
Deleting all your Signal threads at the same time is fairly easy on Android. In fact, it's just as easy as deleting single threads.
On your inbox homepage, long-press on one thread to highlight it, then tap on any additional threads you want to remove and tap the trash can icon. Alternatively, after highlighting the first message, to get rid of all of them at once, tap the square icon with dots around it to select all messages, then tap the trash can. Afterward, select "Delete" on the prompt and you're done.
For some reason, this process is less intuitive on iOS. Sure, it doesn't take very long to swipe left on each conversation to delete them one by one, but if you have a lot of threads, this could be annoying at the least.
So, to delete all of the conversations at the same time in Signal, tap on the cog in the top left of the main inbox screen, then choose "Privacy." On the next page, tap on "Clear History Logs" at the bottom, then "I'm sure" on the prompt.