Changing a Gmail password on an iPhone can be done by first launching the Gmail app, tapping on your profile picture, and then choosing "Manage your Google Account." Next, switch to the Security tab and scroll down until you locate the "How you sign in to Google" section. Here, tap Password and follow the instructions to create a new one. On the other hand, if you are using the Apple Mail app, you will have to re-enter your Gmail password at Settings > Mail > Accounts > Gmail in order to continue syncing the emails after the password change.