Power save on f945 what does it means?

You have entered to activity but you have not started the activity. It will go out of the activity to save power.

https://www8.garmin.com/manuals/webhelp/forerunner945/EN-US/GUID-55A5E621-7A12-47E2-84E6-44CF8F872D79.html 

Default is 5 minutes but can be extended to 25 in the Settings for each activity. 

Also applies if you have paused activity, right?

No, i  was just laying down after just finishing my treadmill run. Like 20mins after it started the countdown when I was at the couch 

Sorry, I meant that suggested power save setting also applies to paused activities. Are you sure you stopped and also saved your activity? I sometimes forget to do the save...

But you had not saved the activity right?  Just stopped it. 

No, i stopped it and saved it as usual. Hadn't had any activity started after i was just laying down when it started the countdown. 

We’ll then it’s likely a ‘ghost’, As noted what you see is a power save timeout. Doesn’t happen when in the default watch face. Either something was pressed accidentally by you or a ghost or perhaps something wasn’t done that you thought was done. 

Nice looking dog by the way