Hydrogen bond
Hydrogen bonds can be intermolecular (occurring between separate molecules) or intramolecular (occurring among parts of the same molecule). Depending on the nature of the donor and acceptor atoms which constitute the bond, their geometry, and environment, the energy of a hydrogen bond can vary between 1 and 40 kcal/mol. This makes them somewhat stronger than a van der Waals interaction, and weaker than fully covalent or ionic bonds. This type of bond can occur in inorganic molecules such as water and in organic molecules like DNA and proteins.
Conjugate acid
We say that the water molecule is the conjugate acid of the hydroxide ion after the latter received the hydrogen proton donated by ammonium. On the other hand, ammonia is the conjugate base for the acid ammonium after ammonium has donated a hydrogen ion towards the production of the water molecule. We can also refer to OH- as a conjugate base of , since the water molecule donates a proton towards the production of in the reverse reaction, which is the predominating process in nature due to the strength of the base over the hydroxide ion. Based on this information, it is clear that the terms "Acid", "Base", "conjugate acid", and "conjugate base" are not fixed for a certain chemical species; but are interchangeable according to the reaction taking place.
The strength of a conjugate acid is directly proportional to its dissociation constant. If a conjugate acid is strong, its dissociation will have a higher equilibrium constant and the products of the reaction will be favored. The strength of a conjugate base can be seen as the tendency of the species to "pull" hydrogen protons towards itself. If a conjugate base is classified as strong, it will "hold on" to the hydrogen proton when in solution and its acid will not dissociate. 
On the other hand, if a species is classified as a strong acid, its conjugate base will be weak in nature. An example of this case would be the dissociation of Hydrochloric acid in water. Since HCl is a strong acid (it dissociates to a great extent), its conjugate base () will be a weak conjugate base. Therefore, in this system, most will be in the form of a Hydronium ion instead of attached to a Cl anion and the conjugate base will be weaker than a water molecule.