Strange loading screen when MBP battery dies and reboots

Solution 1:

This feature is called Safe Sleep. Apple notebooks will keep the RAM contents alive (sleep in PC jargon), but write a copy to the disk (hibernate, in PC jargon) at the same time.

If the battery runs out while the computer is sleeping, when it wakes up, it needs to read the RAM contents from disk, and thus you get the progress bar you are seeing.

Apple doc about it is here

Solution 2:

This is so called "Hibernation" (my first met in windows). When battery dies, the OS dumps whole RAM into HDD (sort of swapping) so that no information is lost. When it's being booted back up, it loads the information back from HDD to RAM (hence you see the progress with those white bars).