What started out as a low budget, deliberate swipe at "Atom Age"-era "mutant ants/atomic scorpions" has turned into a veritable institution.
There have been a number of auteurs who make "bad" movies, realize they have neither the budget nor the talent to produce greatness, and so produce a stream of fun. Troma films produced The Toxic Avenger and any of a number of god-awful sequels, Russ Meyer basically revelled in breasts and bad girls in trouble, and the lovable Ed Wood earnestly made pile of crap after pile of crap in the vain hope that the repeated bashing of the head against the wall will produce another Citizen Kane. Even George Lucas took a cute film about a kid named Starkiller (later renamed to Skywalker) who turned out OK despite not having a dad, except for that bit where he made out with his own sister.
Horror, blaxploitation, kung fu, bikesploitation, and Gidget Go-Go at the Surf Beach type films were staples through the 60s and 70s, and when the home VCR movement created a demand for films, we had tons of guys with machine guns, stupid comedies like "Joysticks" and Revenge of the Nerds, and so forth.
And the idea that a tornado containing sharks would be twice as deadly was unbelievably stupid but unbelievably ENGAGING. The portmanteau word was catchy, and films have been "pitched" with less. An infamous 80s movie got funded based on one photo of two people on motorcycles holding lances, ready to joust - and Talladega Nights had checks hit the table the moment someone started the conversation with "Will Ferrell. As a NASCAR driver." Once you get the check, you stop talking: so that was the entire pitch.
The first was godawful - lighting didn't match the time of day, the special effects were wonky, and they were hamstrung somewhat by the limitation that a shark on land isn't really a threat. But it made money, and by the various laws of Hollywood, more of them got made.
Anchored by the blonde balding dude from Beverly Hills 90210, the trip from his hairline to his eyebrows being a $6.50 cab fare, and Tara Reid, who either can't or won't act - they churn out the same formula by numbers.
Here's a Sharknado movie in a nutshell.
ACT 1 - Before the storm
The lead character, "Fin" (Short for Finley) is somehow trying to warn/get people out of the way of an impending Sharknado (obviously, as of the first).
ACT II - The Sharknado starts
Tons of people get chomped by flying sharks. People close to the main characters are in peril. They're somehow separated and need to find each other, but their cellphones are misplaced/not working/out of power.
ACT III - They stop the Sharknado
Apparently you can get rid of a tornado by detonating something inside it. In the second movie two Sharknados meet and form a super-Sharknado. In the third, the entire eastern seaboard is threatened by a multiple-multiplied Sharknado-wall. Which means a larger and larger explosion, each time. Not sure how they'll top the third, which involves using the Space Shuttle to super-heat the core and when that doesn't work, engaging the SDI ("Star Wars") weapons from space to burn off the entire weather system, just like removing a bad tattoo with a laser. (The fact that anything in the path of the laser would be hideously incinerated, including toddlers and nuns and so forth, is handwaved.)
When the first movie hit the airwaves, celebrities and others LIT UP Twitter and other social media with all manner of commentary. Just about everyone joked about writing the sequel before the first movie was even over, or wanting to be in the inevitable sequel. As a result, repeats of the broadcast were a huge hit for SyFy.
Also as a result, cameos abound. You're as likely to find Kelly Osbourne as a stewardess as you are to find Ann Coulter as the vice president, to president Mark Cuban. George R R Martin of Game of Thrones fame is briefly seen being eaten in a movie theater, someone hired Bill Engvall as the chief of security for the White House and Tara Reid's mom is Bo Derek. Almost all of the cameos are exceedingly brief: some people play themselves, including Joan Collins, Al Roker, and so forth. And almost NOBODY minds that their character's life expectancy - whether ended by shark or the story moving on from them - is the same as a chocolate eclair in Al Bundy's shoe store. This is a modern Cannonball Run movie, where showing up, hamming it up, and walking off is part of the whole "thing". As the movies picked up, more and more people were happy to devote an afternoon to the cameos, so you really have to watch each frame to potentially catch another slumming celebrity.
And of course, Fin's dad turns out to be genuine hero David Hassellhoff, playing an air force/NASA Colonel.
The movies are formulaic, predictable, silly, as time goes on getting more and more ridiculous in scale (a brief comment towards the end of "Sharknado 3: Oh Hell No" mentions that Charleston, South Carolina has been completely obliterated by a Sharknado. Another character builds a customized weapon set and there's a light saber chainsaw in space (because the double barrelled chainsaw wasn't enough).
But they persist, even though they don't make any tangible sense - because they are unbelievably FUN.
You're not going to get a BBC Edwardian era subtle comedy of manners or Oscar Wildeian wit here. Their idea of a joke is someone trying to reach a Big Red Button and losing limbs due to flying sharks along the way. When his hand is above the button he pauses for effect long enough for a shark to take his remaining arm, leading to him having to limblessly crawl another two feet and hit it with his chin.
Tara Reid has the acting ability of a block of wood, but anyone with a mote of acting ability takes the role dead seriously, and Fin deadpans his way through the whole thing, all square jaw and resolute determination. In an homage to the strong, silent action heroes of the 1980s, he's a man of few words and handy with everything from a pistol to an F-14, and he plays the role ramrod straight. When the President hurls a grenade into the maw of an oncoming flying shark in a move that could only be achieved with CGI, Fin deadpans, "Hail to the Chief."
As does everyone else, but they're clearly having fun and realizing they're not making art, they're making entertainment, so the pressure's off. And it means as the premises get more and more and more ridiculous, the more liberty we give to the suspension of disbelief. At the end of the third film, a character gets swallowed by a live shark IN SPACE to try to retrieve another character who's been swallowed. As the shark crashes and burns to earth, he cuts a hole in it with a light-saber chainsaw, deploys his backpack parachute through the hole in the shark, and lands unharmed on earth. Think about that last sentence for a second. Really think about the sequence of events, here.
The third ends with him naming his son "Gill", because it's that kind of movie. Gill was born inside a shark in space and was handed to his father through a hole cut through said burnt-up shark by a prosthetic chainsaw inside a prosthetic missing hand, before its owner, the child's mother, comes through the hole FULLY CLOTHED. Think about that last sentence for a second. Really think about the sequence of events, here.
There's no spoiler tags on any of this because even if you know what's going to happen, the enjoyment is not spoiled by missing out on the reveal.
Again, they'll keep making these things and keep pressing at the boundaries of what we're ready to believe. But so long as they keep making them as fun, as big, and as exciting as they do, they'll keep making them. They've spawned TONS of imitators, such as "Big Ass Spider", "Three Headed Shark" and so forth, but there will only ever be one Fin, and one Sharknado series.