An Arrhenius acid is a substance that produces a hydrogen ion when dissolved in water, and an Arrhenius base is a substance that produces an OH−, or hydroxide ion.

Hydrochloric acid is an Arrhenius acid as it dissociates into a hydrogen ion and a chloride ion when dissolved in water. Sodium hydroxide is an Arrhenius base as it dissociates into a sodium ion and a hydroxide ion when dissolved in water.

However, this definition cannot be used to describe acids and bases that are not in an aqueous solution or bases that do not contain hydroxide ions.

A broader definition by Brønsted and Lowry defines an acid as a hydrogen ion or proton donor, whereas a base is a proton acceptor.

When hydrochloric acid is dissolved in water, it acts as an acid by donating a proton to water, producing a hydronium ion and a chloride ion. When ammonia is dissolved in water, it acts as a base and accepts a proton from water, producing an ammonium ion and a hydroxide ion.

A Brønsted-Lowry acid will always react with a Brønsted-Lowry base and vice versa. When an acid, for example, acetic acid, donates its proton, water acts as a base and accepts the proton. Acetic acid is converted into a conjugate base, acetate, and water is converted into a conjugate acid, a hydronium ion.

Acids and bases that differ from each other due to the transfer of a proton are called conjugate acid-base pairs. In the reverse reaction, the conjugate acid, hydronium, acts as a proton donor and the conjugate base, acetate, will accept a proton. 

The strength of an acid is determined by its ability to donate a proton whereas the strength of a base is determined by its ability to accept a proton. A stronger acid is more likely to donate a proton than a weaker acid. Likewise, a stronger base is more likely to accept a proton than a weaker base.

The strength of an acid and its conjugate base are inversely related. A strong acid dissociates completely in solution and the resulting conjugate base is too weak to accept a proton. The same applies in the case of a strong base and its conjugate acid.

On the other hand, a weak acid dissociates partially in solution. The conjugate base of a weak acid is also relatively weak; therefore, a mixture of the undissociated weak acid and its weak conjugate base will be present in equilibrium. The same phenomenon occurs in the case of a weak base and its weak conjugate acid.