There are some different definitions for acids and bases, but the most commonly thought of and the one you are probably looking for here is called the Bronsted-Lowry definition. It states that an acid is any chemical that has the ability to donate protons (H+). A proton in the chemical sense is a hydrogen cation, or a hydrogen atom with its single electron removed to make a positively charged ion. So acids will produce protons in solution.
Alkalinity is basically another term for base. A base is the exact opposite of an acid. A base is a chemical species that will accept a proton that an acid has donated. The base will chemically accept the proton and react with it to produce a more neutral species. One of the most common bases is the hydroxide anion (OH-). The hydroxide accepts a proton to become a molecule of water as shown below.
H+ + OH- --> H2O
A buffer is a chemical solution that will resist a change in pH (or the measure of acidity) when an acid or base is added to it. The most common buffers are composed of a weak acid and its conjugate base. That way, if a base is added to the buffer the weak acid will neutralize it. If an acid is added to the buffer the conjugate base will neutralize it. Blood is an example of a buffer solution. It is able to maintain a constant pH even when some acid or base is introduced to the system.