Description of a solute's inability to dissolve into a specific solvent.
Note that insolubility is often a matter of degree where a substance that dissolves slightly (that is, which is relatively insoluble) may be describe as insoluble despite at least some solubility. Lipids, for example, though somewhat insoluble within aqueous solutions, in fact are not completely insoluble, often with at least some molecules of lipid slightly dissolved in the water. A better description of solubility, therefore, is what is known as a material's solubility constant, which can range from quite low (effectively "insoluble") to quite high (quite soluble).
Your digestion of fats requires converting them from a somewhat water-insoluble form, as triglycerides, to slightly more water-soluble forms, i.e., fatty acids and monoglycerides. These products of fat digestion, though slightly soluble in water, are somewhat more soluble in lipid bilayers. This has the effect of pulling those fatty acid molecules that have dissolved in water out of the water, thereby driving a dynamic equilibrium towards the absorption of fatty acids and monoglycerides out of the lumen of the small intestine.
The movement of these lipids into water solution, so that absorption can take place, occurs as a combination of the action of lipase enzymes on fat molecules and a dynamic equilibrium between aqueous solution and what are known as micelles, i.e., the storage structure for fatty acids and monoglycerides within chyme (digestive fluids). A three-way dynamic equilibrium thus exists, each with the same pool of the all but insoluble fatty acids and monoglycerides in the middle, with lipase, micelles, and even the lipid bilayer of intestinal epithelial cells contributing to this pool. Net movement of fatty acids and monoglycerides out of epithelial cells and into the body-as-a-whole, however, drives the depletion of fats and their breakdown products from the digestive tract.
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