What is hydrogen bonding and why does water have a higher boiling point than methanol?

Hydrogen bonding is an intermolecular interaction between a partially positively charged hydrogen atom on one molecule and a partially negatively charged atom on another molecule. The difference in charge is due to the atom bonded to the hydrogen being more electronegative. Water has two partial positive hydrogens and one partial negatively charged oxygen whereas methanol only has one partial positive hydrogen (with the methyl group being unable to take part in hydrogen bonding). From this, a greater amount of hydrogen bonding can take place between water molecules than between methanol molecules. Thus a greater amount of thermal energy is needed to overcome these intermolecular forces for water, leading to its boiling point being higher than methanol.