Abstraction is changing the way something is represented in order to move it beyond its constraints.
This is perhaps best represented by the abstraction of oral language into written form. This abstraction frees language from the constraints of the spoken word - in particular the physical and temporal. It's why we can read the words of Plato and Shakespeare despite the centuries that have passed since they last spoke.
The process of abstraction also changes the nature of what it represents. This uncoupling of constraints impacts both positively and negatively. In the case of language - writing liberates language so that it can be communicated broadly across time and space. At the same time this process removes key elements of its oral base - the social, ephemeral and tonal qualities that are embedded into the spoken word.
The written word takes on a monumental nature embodying permanence and scale in comparison to the fluidity of our oral languages. Stone vs water.
As an aside its interesting to see written text begin to embody more liquidity as the abundance of data and information being produced increases.
One of the most valuable aspects of abstraction is its ability to simplify complicated processes. Nowhere is this more obvious than in Mathematics. Through mathematics the simplification of complicated information and processes has been turned into an art. Extraordinarily complicated calculations and data sets can be crunched down into elegant and often beautiful equations. In doing so we can extend mathematics into increasingly complicated areas - but they're complicated not complex. Complexity is the weakness of abstraction. (see Complex vs Complicated)
At its heart complexity involves uncontrolled change and variation, which tends to wreak havoc on carefully developed complicated systems. The process of abstraction removes many of background, meta and environmental factors as noise in order to improve the signal they have chosen.
Complicated systems are improved by breaking them down into individual parts and components. These can then each be improved which will lead to incremental positive change to the system as a whole. This is the Talyorist or Scientific Management process.
Complex systems don't follow the same pattern, in fact quite often working on the parts separately or in isolation actually damages the system. Improvements to a complex system are made by working on the interactions between parts, rather than the parts themselves.