An acid is defined by the high presence of H+ ions while a base is defined by the presence of OH- ions.
Acids will raise the H+ concentration in a solution and Bases will raise the OH- concentration in solution, how they do so (for most common acid and bases) is slightly different.
In general Acids, strong or weak, donate a proton (H+) to the solution causing a raise in H+ concentration.
Now bases work in two ways, some bases like NaOH contribute an OH- directly causing an increase in [OH-] some bases (most weak bases) however are proton acceptors (generally from water) which leaves behind a OH-