Summarize the following:
It's the purple app with an envelope icon on the front. It's in the top-left corner of the screen. This option is near the top of the menu here. You'll see this link below your name near the top of the "Accounts" page. If you have multiple Yahoo accounts signed into one device, you can tap "Account info" below any name to view that account's settings. It's near the bottom of the account page here. If you've recently signed into the Yahoo Mail app, you may not be prompted to enter a password. If you're using an iPhone with Touch ID enabled, you can scan your fingerprint instead. It's near the middle of the screen. This grey link will appear toward the bottom of the page beneath the Make my account more secure button. You'll enter your password once in the "New password" field and then again in the "Confirm new password" field directly below it. You can check the "Show password" box toward the bottom of the screen to reveal the password you're typing. Tapping this option will change your password for your Yahoo account on all platforms. To verify, sign out of your Yahoo account and then sign back in with your new password.

Summary:
Open Yahoo Mail. Tap ☰. Tap Manage Account. Tap the "Account info" link. Tap Security Settings. Type in your phone's passcode. Tap Change password. Tap No, I want to change my password. Type in your new password twice. Tap Continue.