What is the purpose of the microvilli of the small intestine?
To increase the surface area of small intestine for better absorption of nutrients.
The small intestine (SI) is the site of terminal food digestion and nutrient absorption.
The large intestine only absorb water, produce mucus and form stool. So most of the food must be digested here in the SI. Then the products of the digestion (nutrients) should also be absorbed.
An organ in which absorption occurs so intensely must have large surface area. For this purpose the wall of small intestine have some special characteristics : the folds in wall (plicae), finger like projection (villi) and brush border on apex of the cells (microvilli). Together these three increase the surface area by 600 fold.
A diagram showing folds, villi and microvilli in intestinal wall :