This is a fic based on the Time Loop Files, the format of which was first codified by Innortal on fanfiction.net.
Here's a brief guide.
The basic idea is, one character (the Anchor, usually the main character of a fictional setting) is looping back to the very first moments of their parent series every time either they die or some kind of time limit expires. They of course end up monumentally stir crazy given enough time.
Eventually others start to loop as well.
The reset is not always perfect. Sometimes a loop's history will be different to the "prime" loop, or canonical plot.
"Crossover" or "Fusion" loops also occur, randomly. These can involve the home loopers having a guest, or the anchor for one universe spending time in another, or replacements of one character by another.
Vacation Loops are where the Anchor (or others) decide/s "buck it" and lets off steam by doing whatever comes to mind. There's little or no attempt to maintain the original timeline.

In addition, and particularly more recently, it should be known that this story has a collaborative element to it - people may submit loop ideas or loops, ideally at the Spacebattles thread (a link to the current version of which is on the Trope page), and they may become included.

There's two page image options, thanks to Filraen - the current page image has been edited by the original creator from this work of theirs.. The other one is here:
http://hourglass-vectors.deviantart.com/art/MLP-Loops-466030169

Princess Celestia had a good day. Luna had been going out more often and was becoming quite fond of nightclubs, her dear niece Cadance had formally announced her pregnancy—though, privately, Celestia felt she was too young to be a great aunt—and, of course, Twilight, her beloved former student, had taken on her first student and Celestia couldn't be prouder! Yes, it had been a good day.

Celestia Sol woke up much like she did every day the morning: sun waking her as it danced upon her eye lids. Wait, the sun? Celestia's eyes snapped open to reveal she was in Twilight's old room in the observatory. On the other side of the room was a smaller bed where a small dusky unicorn was drooling on her pillow.

Clearly, it must be Tuesday.

Preread and edited by Stahl, Kinsley, and Jumbled

Princess Cadence and Princess Twilight Sparkle are called to Canterlot to take over two very important responsibilities: The Sun and the Moon

Oh, and just one additional thing.

Placed 8th in the Writeoff.me event for Out of Time

(Now on Equestria Daily Cover Source - MLP Wiki site )

Marble decides to briefly come out of her shell and tries something different with Pinkie's hair.

Art not mine.

This story is a sequel to Fear Me, for My Name is Twaith!

Pinkie decides that with a new friend by her side, it's finally time to put to rest something that has been haunting her for a decade.

Thank you to CommanderBigMac for editing!

A mother will do a lot for her child, even give them up if it meant them having a safer life growing up, despite the obvious pain that comes for the parent.

That pain is something Queen Chrysalis has gone through for eighteen years, but now the time is upon them, and she wants her daughter back. Even if that means invading Canterlot during a royal wedding.

Edited by RC2101_Copey
New cover art was created by the talented Jesuka
Now has a TVtropes page: http://tvtropes.org/pmwiki/pmwiki.php/Fanfic/Change
Go watch the reading by Skijaramaz: https://www.youtube.com/watch?v=Ecqtu_Djrw4

(Featured on 18/10/2015, the first day! Thank you!)

Change is now a printed book, information here: https://www.fimfiction.net/blog/732008/i-got-a-thing-change-is-now-a-physical-book

Twilight Sparkle has made a number of homemade clones to act as her while out with her friends. Why? More time left for the original Twilight to study, of course.

If only she weren't so absolutely terrible at making clones.

Sex tag added due to Sexy Sparkle.