Step 1 - Remembering what are acids and bases
Acids and bases are inorganic functions, i.e., classes of substances which share some common properties.
Bases usually liberate OH- when dissolved in water, while acids liberate H+ in the same conditions.
Both OH- and H+ ions have effects in the human body, specially because they can act as catalysts, i.e., they may accelerate or propitiate several chemical reactions.
Step 2 - Hazards of acids and bases
Being such strong catalysts, acids and bases may accelerate the decomposition of a lot of substances, resulting in corrosion or dismantlement of some tissues, including human tissues, such as skin, muscular tissues etc.
Of course, not all acids or bases are that agressive. It depends on their strenght, which can be measure by the pH scale. Extremes pHs, both high and low, are always dangerous, for they indicate a high amount of H+ or OH-.
Some acids, such as HF, do not harm the skin right away. We won't feel anything, in fact, if it drops on our hand. But it can very easily penetrate the skin, affecting muscular tissues and specially our calcium rich bones, "dissolving" them.
Some acids and bases can't be handled daily. Their sale are either controlled by the government of by the army. Some other substances demand training so you are aware of how to manipulate and deal with them.