The closing line is actually a big blob of beeswax and resin plopped onto the parchment, then smooshed down with the royal seal and left to dry. That's how they signed thing back in the olden days…and it's actually kind of brilliant.

Anybody can forge a signature, especially when handwriting wasn't really a skill taught much outside of monasteries, but it's much more difficult to recreate a big metal stamp. So the king had the only copy of the royal seal and would smack it down into wax every time he wanted people to know that he approved of something. Likewise each noble and bishop and important person would have a one and only copy of their seal too.

The actual closing words of the Magna Carta are:

Given by our hand in the meadow that is called Runnymede, between Windsor and Staines, on the fifteenth day of June in the seventeenth year of our reign. (63.4)

…which is basically the lead up to a signature/seal. You know that it's the king speaking because of the way he refers to, "our hand." Only kings can get away with talking about their body parts like that (in the majestic plural).

Also, the king's hand probably didn't do much of anything noteworthy at Runnymede. It's very unlikely that anyone actually named in the Magna Carta physically wrote on the parchment. They were all wealthy, celebrity types who surely paid some scribe to write as they dictated.