There are three theories of acids and bases. These are Arrhenius, Bronsted – Lowry, and Lewis, each named for the person (people) who developed the theory.
You can think of representing these theories in a Venn Diagram composed of 3 concentric circles. The innermost circle is the Arrhenius theory which was the first of the three theories and explains the behavior of a special class of acids and bases. The next larger circle, containing the Arrhenius circle, is the Bronsted-Lowry theory which is larger because it explains the behavior of a much larger class of chemicals. Finally, the outer circle is the Lewis theory which explains the acid and base properties of all chemicals and encompasses the other two theories.
In 1886, a Swedish chemist named Svante Arrhenius proposed the idea that an acid is a chemical which releases a Hydrogen Ion when it is dissolved in water and a base is a chemical which releses an Hydroxide ion when dissolved in water.
{for an animation of how this works, see also our post on strong and weak acids}
This is a fairly detailed video about Arrhenius acids and bases and slats. Its worth watching but be sure to take notes!
Next comes the Bronsted-Lowry theory