The earliest experiments to understand the nature of acids and bases were concerned with substances that would either increase hydrogen ion (proton) H+ concentration or increase hydroxide ion (HO-)concentrations in aqueous (water) solutions. These substances were termed acids and bases respectively. For example bubbling HCl gas through water increases the H+ concentration (decreases pH) in aqueous solutions therefore it is an acid. Likewise, NaOH is considered a base since it increases the -OH concentration (increases pH) when added to water.
At the time of these studies it was not known that protons, H+ ions, do not actually exist as bare naked protons, but rather form hydronium ions in solution. We should point out here that a bare proton is simply an empty 1s orbital. In a hydronium ion the empty 1s orbital of the proton interacts with lone pairs of a water molecule forming a covalent bond. We would show this reaction as follows.
The Arrhenius definition was important since it provided the concept of protons (H+) as acids and hydroxide ions (-OH) as bases. The Bronstead-Lowry definition of acids/bases provides a more complete definition in which substance are classified as acids if they donate a proton and bases if they accept a proton. It also introduced the idea of conugate acids and bases. In this definition, upon donating a proton, the acid become the conjugate base. The base becomes the conjugate acid. The conjugate acid and conjugate base are the acids and bases in the reverse direction. The following example of acetic acid in water shows its conjugate acids and bases.
The Lewis acid and base concept is very important in organic chemistry. Many of the reactants and intermediates we use in organic chemistry are best understood within this definition. While the Bronstead Acid/Base definition is concerned with protons, the Lewis definition is more concerned with electrons. As you will find out in the next section Lewis acids are electron pair acceptors (i.e. empty orbitals or electron sinks) and Lewis bases are electron pair donors. Lewis acid definition does not mention nor is it concerned with the protons. Lewis acids don't need to have protons (e.g. BH3, BX3, AlX3 and FeX3).
For example, tetrahydrofuran (THF) a Lewis base reacts with BH3 which is a Lewis acid.