If you've ever connected your iPhone to a computer before, iOS would prompt you to "Trust" the computer and enter your passcode to confirm. According to Apple, trusted computers can "sync with your iOS device, create backups, and access your device's photos, videos, contacts, and other content." This is a lot to give a computer access to, especially if you do so with one you don't want to always trust.
When you leave your iPhone on a table or anywhere within somebody else's eyeshot, a private message may pop up on your lock screen that could be read by anyone who sees it. But there's a way to keep others from reading your possibly sensitive text messages and emails without giving up the convenience of lock screen notifications entirely.