When LG announced the G5, one of the headlining features outside of its modular design is the always-on display. Yet, out of the box the feature isn't enabled, which is likely to confuse users.
To enable the G5's always-on display, launch the Settings app, then select Display from the list of options at the top of the screen.
Next, scroll down until you find the setting for Always-on Display. You can slide the switch next to it to the On position, or you can tap on the three dots to the left of the switch to turn it on and customize the feature.
Currently, the only customization option is to have either the current time or what LG calls a "Signature" on the screen. Time will naturally display a digital clock, while signature will display some text. The feature defaults to your name, and it indeed makes it look like you signed the screen of your device thanks to a fancy font. However, you can alter the text and font to say whatever you want during the setup process.
With LG's always-on display enabled, any time your device is locked the screen will remain on, albeit at a very low brightness. When the device is in a purse or pocket, however, the feature automatically turns the screen all the way off to preserve battery life.
Otherwise, the time or signature, date, and any pending notifications will be shown at all times. You can't read the contents of an alert, but you can quickly and easily identify which app(s) have a new notification and decide if you should unlock your phone or if it can wait.