What happens
Capillary action comes from the balance between adhesion to the solid surface, cohesion within the liquid and surface tension.
Water wets clean glass well, so in a narrow glass tube it forms a concave meniscus and rises above the surrounding water level. Mercury behaves differently on glass and forms a convex meniscus.
What changes the process
The narrower the tube, the more important the surface becomes relative to the amount of liquid, so capillary height can become larger.
Why it matters
Paper towels and porous materials use the same family of effects: interconnected small spaces draw liquid through the material. In plants, water transport is more complex and cannot be reduced to capillarity alone.