The term was coined by a couple of writers more studied in the subject than me, but I'll summarise it here.
Imagine that you had to build something to carry loads over a long distance. Imagine having to reinvent the wheel, the axle, the cart bed--
Or imagine trying to calculate something and having to recreate differential calculus from the ground up.
You'd never get anything done. By the time you finished recreating differential calculus, you'd be an old man going through philosopause.
No. Instead, you'd go to the library and dig up the books you need to find out about differential calculus (or possibly how to make a better cart).
Intelligence is the knowledge inside your head.
So what is extelligence? That would be the knowledge outside - the knowledge that we keep in books, or online, or even passed on by word of mouth.
Extelligence is libraries.
Language enables me to pass knowledge to you, and vice versa, but language alone is not extelligence. Extelligence must be non-volatile; it must be able to not only pass from me to you, but to your children and grandchildren and so on until you and I are both long dead.
Extelligence is the intelligence of those long past, encapsulated where we can access it, and what we learn will become extelligence for those that follow.
Of course, it may not always be right. That's why I protest so much against those who lie in service of an agenda.