An example of a strong acid is hydrochloric acid (HCl) which is produced in the stomach to form the gastric acid that digests food. This is produced by the parietal cells of the stomach; these have membrane proteins that expel H+ (proton pump) and Cl- (transport channel) ions into the stomach to produce this acid.
An example of a base in the human body is bicarbonate (HCO3-), which helps maintain the body's pH and thus homeostasis. Bicarbonate neutralizes the carbon dioxide (acid) in the bloodstream, preventing the pH of the blood from decreasing. If CO2 decreases the pH increases due to HCO3-.