Water has a high heat capacity because a lot of heat energy is required to break the hydrogen bonds found in a molecule of water. Because the majority of heat energy is concentrated on breaking the hydrogen bonds, the water molecule itself heats up after the bonds are broken.
Once the hydrogen bonds in a water molecule are heated up enough to break, the additional heat energy can then be imparted to the water molecule itself. This additional heat energy then vibrates the water molecule, allowing it to bump into nearby water molecules to distribute the heat energy imparted by a heat source. However, the process of heat energy distribution is slow, as the vibrating water molecule must impart sufficient heat energy to break the hydrogen bonds in the surrounding water molecules. Once the heat source is removed from the water it cools down, but very slowly.
Just as significant energy is required to break the hydrogen bonds in a water molecule, significant energy is likewise required to re-form them. Only when the water molecule achieves a low enough temperature to allow the hydrogen bonds to re-form does the water molecule release the heat energy. This process of warming and cooling explains why water slowly heats up and cools down.