Define acids and alkalis in terms of proton transfer, acids as a source of H+ and alkalis a source of OH-
Acidity is caused by the presence of H+ ions, these ions form when a chemical dissociates in water. What this means is that the water separates the Chemical i.e. HCl into H+ ions and Cl- ions, as shown in the below diagram. To do this the HCl gas is bubbled through the water
It is the presence of these H+ ions that make a substance acidic, the more H+ ions in relation to the other ions, the more acidic the solution will be.
This is why pH stands for Percentage Hydrogen, or Part Hydrogen, meaning that it shows how much Hydrogen there is in the substance (Hence why the H is capitalised because it is the elemental symbol)
Alkalinity is basically the same principle, except instead of dealing with H+ ions we are now talking about OH- ions. So for example if we take Sodium Hydroxide and place it in water we can see that it dissolves and dissociates to form OH- ions and Na+ ions, as shown in the diagram below.