An abstract machine is a model of a computer system (considered either as hardware or software) constructed to allow a detailed and precise analysis of how the computer system works. Such a model usually consists of input, output, and operations that can be preformed (the operation set), and so can be thought of as a processor. Turing machines are the best known abstract machines, but there exist many other machines as well such as cellular automata.
Abstract machines that model software are usually thought of as having very high-level operations. For example, an abstract machine that models a banking system can have operations like "deposit," "withdraw," "transfer," etc.