There's nothing worse than fighting tooth, nail, and banana peel for first place in Mario Kart, only to lose it because a blue shell decided to saunter up and explode on your parade. Would you believe, though, that it's actually one of the best things about Mario Kart?
This video by Extra Credits does an excellent job of breaking down why the blue shell is so integral to, well, pretty much everything about Mario Kart. Most obviously it's The Great Equalizer—the soaring blue embodiment of pure carnage that gives players at the back of the pack a fighting chance—but that's only the tip of this spiky, 'splody iceberg.
The blue shell handily takes care of one of Mario Kart's biggest problems: being in first place is actually really boring. No longer are you hurling items and butting heads with rivals. Instead you're probably holding onto a weak item to guard your position and trudging ever onward while very little actually, you know, happens.
The blue shell introduces an element of struggle to maintaining the lead, but not in such a way that, say, the second place player can nab a blue shell and take a huge lead by sheer luck. It's all about those way in the back. It appears only (well, mostly) when it's needed.
That's all well and good for players just looking to have harmless fun, but what if you're a Serious 'Karter with a tattoo of Luigi's death glare emblazoned on your heart? Doesn't that take away an element of true skill from the game? Yes and no. Avoiding the blue shell is a skill unto itself, often a matter of perfectly timed item usage or strategic maneuvers to, say, back into other people or train the shell on whoever's in second.
The short version? Nintendo puts a lot of thought into this seemingly reckless force of nature, and it shows if you're willing to dive just a bit below the surface.
I still hate it, though—at least, when it happens to me. I don't think I've cursed at a single item in any other game more. Well, unless you count the whole of Mario Party (and really just everything having to do with Mario Party).
If you can't get enough blue shell elucidation, I also recommend this crazy history/existential thought piece/epic poem by Ian Bogost. He says things like "This is the Blue Shell of collapse, the Blue Shell of financial crisis, the Blue Shell of the New Gilded Age" and "The Blue Shell is the cruel tax of gaming, the welfare queen of kart racing." It's... yeah, just read it.