What is the "mucin net"?
From Wikipedia (emphasis mine):


  Mucins are a family of high molecular weight, heavily glycosylatedproteins (glycoconjugates) produced by epithelial tissues in most animals. Mucins' key characteristic is their ability to form gels; therefore they are a key component in most gel-like secretions, serving functions from lubrication to cell signalling to forming chemical barriers.


The "ability to form gel" is the key here. Also from Wikipedia:


  Gels are defined as a substantially dilute cross-linked system, which exhibits no flow when in the steady-state. By weight, gels are mostly liquid, yet they behave like solids due to a three-dimensional cross-linked network within the liquid.


So, a gel (and mucins are no exception) is composed of a liquid trapped in a 3D net, much like a sponge. This is the "mucin net" your book is referring to.