Fluff is it important?

Yes of course it is! It is the reason you start an army in the first place! Or it is just because you like the look of special marine? For example when I saw the Black Templars on Bolter and Chainsword I was sold! Tabards, chainswords and bolt pistols,... All together fighting to purge the unclean and kill the heretic!?  Just look at the pic below? After reading Hellsreach I felt more zealous then ever before. That book made me want to kill some orcs!

Black Templars by Ron, From the Warp

Of course you can write the fluff for your army all by yourself. Which I did for my Templars!
The Aurum Crusade is the crusade against Alpha Legion and World Eaters. It was an force greater then anything ever seen. So Blood Angels, Space Wolves and Black Templars united to defeat them! Because the slaughtering made daemons appear. The Grey Knights came to help their brothers.
The reason I let the Blood Angels and Space Wolves "help" is because this is my way of making a squad unique. One squad has wolf pets cause they aid the Space Wolves and another got Blood Angels stuff.

Gameswork Shop

But how does Games Workshop work this in the codex? Well they take a few big fights and jam them in the codex. That sometimes is enough for a player to get going! Or it could be just the look of the army that makes the player wanna go all Waagh or heretic! But the fluff! The idea of not knowing what is behind the Angels Sanguine their helmets or the hate against pyshic powers in the Space Wolves codex. The slaughter of the Tyranids against the Ultramarines their homeplanet.... Those are all reasons to just make that army!

Gameswork Shop

The entire fluff of the 40k Universe? Is it important? Of course it is!? Without it we would be nothing. Their wouldn't be any armies at all! There wouldn't be any hobby to begin with...
Now for example what if 40k was 50k? And for example the Blood Angels where all gone! And that Abaddon conquers Terra? That 40k goes to 50k is more likely to happen then that easterday is on thursday. No, for example what if it was Dorn who betrayed the emperor? (See the Dornian heresy for what would happen) Or that the lost primarchs where found? It would (have) change(d) everything!

Black Library

The Horus Heresy and Black Library! How much people did not enjoy the books? Alot of folks did!
It is also the reason why there are some 30k / heresy Armies! Like a Son Of Horus legion or an Emperor Childern army. Like I said first the story in the book makes you wanna start an army. I myself wanted to paint Lucius and Typhus after reading the books about their Legion.

Is fluff important? Yes it is!
- It is the key point to maybe start an army!
- It is the part you read when you get a new codex!?
- Its something you write for your own army
- Its is a reason to paint some new models
- Make just one squad of that army to honor them
- ....