What about bases though? Day-to-day, the term "base" is often used interchangeably with the word "alkali".
Although their methods are slightly different, both alkalis and bases increase the pH value of a solution by reducing the concentration of H+.
To illustrate the differences in the action of alkalis and bases, have a look at the picture on the right of a beaker of acid. Note that there are more H+ ions than OH- ions. When alkali (free OH- ions) are added, the solution is initially neutralised. Then as more alkali is added, it becomes alkaline.
A base, however, is a molecule other than a OH- ion which can bind to free H+ ion.
So, a basic solution does not add more OH- ions to the solution, it just removes the extra H+ ions.
When a base is added to the beaker of acid, note that the concentration of H+ decreases but the concentration of OH- does not increase.
In summary, a base is a molecule which can bind to free H+ ions.