Adhesion is responsible for a meniscus and this has to do in part with water's fairly high surface tension. Water molecules are attracted to the molecules in the wall of the glass beaker. And since water molecules like to stick together, when the molecules touching the glass cling to it, other water molecules cling to the molecules touching the glass, forming the meniscus. They'll travel up the glass as far as water's cohesive forces will allow them, until gravity prevents them from going further. Cohesion is an intermolecular attraction between like molecules (other water molecules in this case).
