There are different ways of describing pH or acidity/alkalinity at a molecular level, even at university degree level. Probably the simplest way is to describe it is in terms of the levels of positively charged ions in a solution.
Chemicals in solution frequently dissassociate into charged ions For example, as everybody knows the chemical formula of common salt is NaCl. In water, however, it breaks up into Na+ and Cl-. An acidic chemical, such as hydrochloric acid HCl breaks down into H+ and Cl- in solution, and it is the positively charged hydrogen ions (H+) that cause acidity (acidity really being nothing more a name than certain chemical's ability to cause a particular type of chemical reaction). The higher the level of H+ ions, the the more acidic the solution and lower the pH.
H+ ions can be counteracted and cancelled out by negatively charged 'OH-' ions, however. A chemical with high levels of OH- ions is called alkaline, as it tends to cause the opposite type of reactions to an acid.
This is why there is a separation between 'acid' and 'alkaline', even though they are just different parts of a spectrum of chemical activity. An acidic solution has more H+ ions than OH- ions while an alkaline solution would have more OH- ions than H+ ions. Water is exactly neutral because it has exactly equal numbers of H+ and OH- ions (H+ plus OH- = H2O!).
Hope this helps; it is a bit wordy and simplistic at the same time! Perhaps other more knowledgable users can step in and clarify things?