Some phones have a small secondary display that can show the time, new notifications, and other information while the phone is otherwise idle. This smaller display uses less electricity than the main display, allowing it to be always-on without hurting the phone's overall battery life.
On a modern smartphone, the second display might be on the front, above the main display, or on the back.
Many old-style clamshell phones have secondary external displays on the outside, so that the user can see who is calling before opening the phone to answer an incoming call. The display therefore shows Caller-ID information during an incoming call. Most such phones use this display to show the time and/or status at other times.