The definitions of acids, bases, and the ph scale that measures their relative strengths, is fundamental to the understanding of chemistry.
There can no better place to start with chemistry than to master these concepts.
At the most fundamental level you can think of relationship between three common household substances. Lye (NaOH used for cleaning ovens), Hydrochloric Acid (HCl used for cleaning carbonate build up from taps and kettles) and Table Salt (NaCl used for seasoning foods).
Lye and Hydrochloric acid are two very powerful cleaning agents used for changing undesireable solids into liquids that can be washed away.
Rather than increasing their power by adding them together; we literaly neutralize their power; and in the process create common salt, which in a purer form, we would be happy to eat with our french fries. (Don't try this at home!!)
Keeping this simple picture in mind, may help you as you work towards visualizing the significance, and the interaction, of acids and bases.
If you are interested in knowing more, we have another article which includes a description of the Brønsted-Lowry and the Lewis definitions for acids and bases.