BOTH ADHESION AND COHESION ARE DEMONSRATED IN THE ABOVE IMAGE. Image from NOAA
Cohesion: Water is attracted to water. Observe the cohesive effects of water molecules permitting a drop of liquid to form on the leaf above and maintain a spherical shape that will roll on a surface without breaking apart. The lowest energy state for this drop occurs when the maximum number of water molecules are surrounded on all sides by other water molecules -- meaning that the drop should have the minimum possible surface area, which is a sphere. More precisely, the positive and negative charges of the hydrogen and oxygen atoms that make up water molecules makes them attracted to each other.
In a water molecule, the two hydrogen atoms aligmn themselves along one side of the oxygen atom, with the result being that the oxygen side has a slight negative charge and the side with the hydrogen atoms has a slight positive charge. Thus when the positive side on one water molecule comes near the negative side of another water molecule, they attract each other and form a bond called a hyrogen bond.
Hydrogen bonds cause water to be highly attracted to each other. Therefore, water is very cohesive.
See also: Why water is such a good solvent.
Adhesion: Water is attracted to other substancesAdhesion is the attraction of molecules of one kind for molecules of a different kind, and it can be quite strong for water, especially with other molecules bearing positive or negative charges. Chemical adhesion occurs when the surface atoms of two separate surfaces form ionic, covalent, or hydrogen bonds. There is no single theory covering adhesion, and particular mechanisms are specific to particular material scenarios.
.."Capillary action occurs because water molecules bond each other strongly due to forces of cohesion and adhesion where water molecules are attracted and stick to other substances such as glass or paper.
Adhesion of water to the surface of a material will cause an upward force on the liquid. The surface tension acts to hold the surface intact. Capillary action occurs when the adhesion to the surface material is stronger than the cohesive forces between the water molecules. The height to which capillary action will take water is limited by surface tension and gravity..." see Capillary Action