It's not finger knitting (although some do call that chain knitting) - it's a technique developed by Lisa Gentry to combine some crochet-like sections with knitting.
From http://knitting-patterns-techniques.suite101.com/article.cfm/chain_knitting :
"Having said that, what exactly is chain knitting? Imagine knitting along as usual, and then adding crochet chains wherever they are desired; at the cast-on, right in the middle of the knitting, or at the end. The technique, at its most basic level, can be described as knitting in the normal way, occasionally putting the knitting needles down, grabbing a crochet hook, and adding chains to the knit work. However, Gentry has created the procedure in such a way that the knitter continues to use knitting needles all the way through the project; no crochet hooks are necessary."
Her site at http://www.hookandneedledesigns.com/ has more information on the book.