Penny turns green with vinegar
This question may explain about what happens with the pennies at a microscopic level: What is the product of a copper and vinegar reaction?

Also, in his paper, Stephen DeMeo presents the electrochemical perspective:


  The mechanism that has been proposed involves the formation of a free radical and an electrochemical corrosion process (1). [...], suffice it to say that the mechanism does involve formation of a strong oxidizer, peroxoacetic acid ($\ce{CH3COOOH}$), from dissolved oxygen, as well as the production of a copper oxide and a copper ion.


He also explains why the reaction just happens in the presence of oxygen:


  Since copper is below hydrogen in the electrochemical series, copper is reluctant to displace hydrogen ions from electrolytes.  In terms of standard electrode potential, copper has a potential of 0.34 volts ($\ce{Cu -&gt; Cu^{2+} + 2e-}$), while hydrogen has a greater potential of 0.00 volts ($\ce{2 H+ + 2e- -&gt; H2}$). The electromotive force of the cell would be negative and therefore the reaction would be nonspontaneous under standard conditions. When oxygen is involved in the reaction between copper and acetic acid, the electrochemical series and the standard electrode potentials cannot be used as a guide to determine if the reaction is spontaneous.  A generalized relationship between copper metal and acids is nicely described by Massey: "Although copper metal will dissolve readily in an oxidizing acid such as nitric acid it will not dissolve in a nonoxidizing acid unless either an oxidizing agent or a suitable complexing agent is present also" (6).



Reference: DeMeo, S. Does Copper Metal React with Acetic Acid? J. Chem. Educ. 1997, 74, 844-846. DOI: 10.1021/ed074p844