There are two main contexts for defining an acid or a base. These are the Brønsted-Lowery definition and the Lewis definition.
The Brønsted-Lowery definition defines a base as a proton acceptor and an adid as a proton donor.
General Brønsted-Lowery acid - base reaction
The Lewis definition defines a base as an electron pair donor and an acid as an electron acceptor. A Lewis base has a pair of non-bonding electrons which it can use in forming a bond to a Lewis acid.
General Lewis acid- base reaction
Many molecules have the ability to act as an acid or a base, this type of behaviour is termed amphoteric behaviour. Water and alcohols are examples of amphoteric molecules. If a strong acid is added to water the water will be protonated and become H3O+ and if a strong base is added to water the water will be deprotonated and become HO-. Therefore in the first instance the water acts as a base and as an acid in the second instance.
The following reaction mechanisms show firstly, water acting as a base with a strong acid, HCl, and then acting as an acid with the base ammonia.
However one must realise that all compounds can express amphoteric behaviour to a certain degree. As with a strong enough acid almost any compound will be protonated and with a strong enough base almost anything can be deprotonated. However some compounds have more of a tendency to act amphoterically
Amino acids are another example of amphoteric molecules, however they are amphoteric by different means. An amino acid contains two different groups, an acidic group and a basic group. When ammonia is dissolved in water the acidic end (COOH) protonates the basic end (NH3) of the molecule
The next page discusses the strength of bases