The Clausula de Rescision system has existed in La Liga for a while now. But it gained more traction after the Webster and Bosman rulings in the 1990s. Basically under common Human Rights standards, players have equal freedom of movement - for better living status, working conditions and so forth within the boundaries of the Union. And after the Andy Webster case, FIFA's Regulations for the Status and Transfer of Players added Article 17 which states that any player who signed a contract before the age of 28 can buy himself out of the contract three years after the deal was signed, which is shortened to two years if the player is 28 or over. This kind of parlays into the current clause system wherein the players can buy out the remainder of their contract and the existing deal in unilaterally terminated, or the player qualifies for certain terms in the contract literature.
All this created a legal mess and potential player strikes for European clubs, necessitating a uniform predetermined system. So the Clausula is essentially a sort of middle ground between the club and player unions, a sum of money which protects both the employer (they can recoup their investment even if it doesn't necessarily reflect current market value - could be argued Laporte's clause is way above his actual value, are safeguarded against derisory bids - Javi to Bayern) and the employee's (a player at a smaller club wants to play for a bigger club - not just Spain, but in the Bundesliga too - like Marco Reus, wants a hassle-free escape - Gotze, wants to play in Europe, wants more first team football - Thiago) monetary and labor interests.
As for Barcelona and Real having astronomical buyout clauses, it's a) mostly done as a formality and rarely if ever are the clauses actually paid - eg. Fabregas had a clause of €200 million, Alexis Sanchez had €100 million or b) a precedent has been set because of the Figo transfer where Perez and Madrid simply activated his Clausula de Rescision, and because the player agreed personal terms, Barcelona had no say in the matter as the selling club. Now those clubs want to absolutely ensure their best player aren't poached, hence ludicrous clauses, apart from cases like Thiago where he didn't play enough first team football which in turn triggered a lower release clause stated in his contract (€90 million reduced to ~€20 million).
Dunno why English clubs don't always employ a similar approach though. Maybe the club and player unions can't reach an agreement on a larger league-wide scale, or maybe there's a disparity in terms of valuation, or maybe they just want to wing it ? Though even apart from Suarez and Fellaini, certain individual players have release clauses inserted into their contracts in England (generally at smaller clubs) which have been agreed upon by the selling club and the representatives of the player at the time of signing/ renegotiation :
Joe Allen :
http://www.theguardian.com/football/2012/jul/25/swansea-liverpool-joe-allen
Demba Ba :
http://www.bbc.com/sport/0/football/20890803
AFAIK Anelka had a clause in his Arsenal contract when he wanted to sign for Real Madrid ?
This apart from players above 28 free to buy out the remainder of their own contract under the Webster Ruling (IIRC Cabaye threatened to buy out his contract at Newcastle).