It was 2 parts - One, he took a buyout, considering he had (reportedly) $25 million on the contract, which he absolutely would have been owed if he were fired. So, much like Brady wanted the 'no franchise tag' clause in his last deal, he took a little bit less than that (and Kraft obviously loves that), that leads me to -
2) Guarantee that they wouldn't seek compensation should Belichick coach elsewhere. That's a much bigger part of this - Belichick's not going anywhere without as full an arsenal as possible at his disposal.