I really don't get what is so great about twin laser turrets. What am I missing?

Ultra-consistent damage, and a great range-window.

No range 3 bonus die against them, too. Also, obviating evade tokens as a means of reducing incoming damage on attacks which are guaranteed to hit anyway, which is always irritating.

Not to mention potential double stress with Tactician.

It's a really consistent 2 damage you can chip away with turn after turn.

Like the accuracy corrector it puts the pressure on the green die to keep you alive, and we know those buggers will fail you more often than not.

They came to life in a response, it would appear, to counter high hull/low agility ships. At one time, the "Fat Han" build of a fully equipped Millennium Falcon was dominating the scene (thanks in part to a certain protocol droid), and it was difficult to take them out efficiently. Thus, enter the Twin Laser Turret. By having the ability to be handled as two attacks, it could chip away at the MF and C-3P0 each turn, and even faster if you had more than one of them. Eventually, it was realized that you can equip four Y-Wings (and their corresponding 8 total hull/shield points) with TLTs. Lots of health, and pretty consistent damage each turn - if boring to fly against from the Red Dice Swarm.

Pros: turret weapon, three dice, secondary so range defense bonus from the defender
Cons: 6 points, only works at range 2 and 3, some people consider it a very "cheap" way to play

They deal significant easy damage to low agility ships, yet also exploit imo x-wing greatest flaw: green dice. Any high agility ship (like fel) rely somewhat on green dice. Green dice always fail, the only real question is when. TLT accelerates that path quicker by allowing double the rolls.

Things like autothrusters do help quite a bit, but take Slugrage's example of 4 y-wings with TLT. How many rounds can even a ship like whisper survive 8 attack rolls? Only 4 need to connect.

If you still aren't convinced watch videos of worlds Matchups on YouTube and it becomes pretty clear.

Against low to mid agility it's pretty much an R2-3 autoblaster turret, and it's pretty good at hitting high agility with modification too.

A nice high agility killer is Latts paired with two ywingd with R4 Agromechs. Pretty quick work of soontir and Poe.