The cohesiveness of water means that water molecules attract other water molecules (the prefix "co-" means "together"). The cohesiveness of water molecules is due to the polarity of water molecules. Polar molecules demonstrate slight positive and negative charges. This is due to electronegativity differences. Electronegativity is the affinity of an element for electrons. Spcifically, the electronegativity of the oxygen atom within water has an electronegativity of 3.5. The electronegativity of water's hydrogen atoms is only 2.1. Since oxygen has a higher electronegativity than hydrogen, the electrons are pulled towards the oxygen more. This results in the oxygen having a slightly negative charge and the hydrogens having a slightly positive charge.
Opposite charges attract. Therefore, when two different water molecules are next to one another, the oxygen of the first water molecule will attract the hydrogen of the second molecule. This is how hydrogen bonds are formed. The result is the cohesion amongst water molecules.