By default, the screen of the Apple Watch is set to turn off after 15 seconds of inactivity. However, you can tweak your settings to keep your screen awake for longer periods of time.
Here are the instructions on how to adjust the screen timeout settings of your Apple Watch (WatchOS2 required).
Configure the Sleep Settings of the Apple Watch
This option can be configured from the Apple Watch app installed the companion iPhone or iPad. Go to My Watch > General > Wake Screen > On Tap. Two presets are available: Wake for 15 Seconds and Wake for 70 Seconds.