Quote Originally Posted by bovi
An acid is a molecule that when mixed with water will release a proton, creating a H3O+ molecule. These unfaithful protons can also react with a number of other materials.

Similarly, a base is a molecule that when mixed with water will absorb a proton, creating an OH- molecule. Bases also can react with a number of other materials. One of the most basic (in every sense of the word) bases is NaOH, which simply will dissolve into a Na+ ion and a OH- one, so while it won't react with the water molecules per se it will still produce a OH-.

An acid will "cancel" a base because the acid will release its proton and give it to the base, fulfilling its "desire" for the extra proton.

There are also buffer molecules, that are willing to absorb or release protons depending on the abundance of either OH- or H3O+ ions in their environment. A basic buffer is HCO3-, which is originally made up of carbonic acid (H2CO3, composed of carbon dioxide (CO2) and water (H2O)) which has released one proton. It is liable to release another proton and become CO3-- in basic environments but will absorb an extra proton and become H2CO3 in acidic environments. H2CO3 is incidentally liable to dissolve, releasing CO2 gas, and is used in "soda" drinks like Coca Cola.

Just a technical note, what Bovi described above while correct is only a subset of acids called Brønsted-Lowry acids. There are also acids that don't involve releasing a proton, but instead accept electrons. These acids are called Lewis acids. All Brønsted-Lowry acids can be described as Lewis acids, but not the other way around. Also of interest Lewis acid-base reactions can occur outside of an aqueous environment.