I think the answer should be the fact that water is a polar molecule.
This means it will attract other molecules which are polar (adhesion), including itself (cohesion).
I'm not sure about the last part of the question (high specific heat capillary action, the wording is a little confusing), but I think the reason why water has a high specific heat is the hydrogen bonds. Hydrogen bonding is the strongest kind of bond you can have in a molecule, so it would be harder to break those bonds, even with high heat.
Answer:
The polarity of water
