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Acids and bases are compounds (or molecules) Compounds are atoms of 2 or more elements that have an ionic bond. 

The compound HCl (Hydrogen and Chlorine) is an acid. 
To form the compound the Hydrogen atom, which has one electron in its valence shell, gives off its electron to the Chlorine atom which has 7 electrons in its valence shell. This forms an ion of Hydrogen and Chlorine. The Hydrogen lost a neg. charged electron so it has a positive charge. It is a positive Ion, the Chlorine gained a neg. charged electron so it is a Neg. Charged Ion. 

An acid yeilds Hydrogen ions when put in solution. 
When HCl is put in solution, it the ionic bond is broke and the H+ is yielded which makes this an acid. 

A base accepts H+ ions. 
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When hydronium ion is mixed with water we get acids
when hydroxide is mixed with water we get base
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