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D E F I N I T I O N S

analogy - A systematic comparison between structures that uses properties of and     relations_between objects of a source structure to infer properties of and relations     between_objects of a target structure. (Dictionary of the Philosophy of Mind) 

1: inference that if two or more things agree with one another in some respects they will prob. agree in others
2a: resemblance in some particulars between things otherwise unlike: similarity b: comparison based on such resemblance
3: correspondence between the members of pairs or sets of linguistic forms that serves as a basis for the creation of another form
4: correspondence in function between anatomical parts of different structure and origin (Merriam-Webster Dictionary Online)

Analogy is a basic human reasoning process used in science, literature, art, education, and politics. Analogy can be used to make predictions, provide explanations, and restructure our knowledge. Analogy is also used to influence public opinion, fight battles, win wars, start and finish relationships, and advertise laundry detergent. (Kevin Dunbar)

 
Terminology 
 
Dr Kevin Dunbar, professor of psychology and cognitive science at Dartmouth college, provides the following information on terminology for analogies: 

Different researchers on analogy use different terminologies, however most researchers distinguish between two main components of an analogy -- the Source and the Target. The Source is the piece of knowledge that one is familiar with. The Target is usually the less familiar piece of knowledge. When one makes an analogy, one Maps features of the Source onto the Target. In the case of the Earth-Mars analogy, the Source is the Earth and the Target is Mars. By Mapping features known about the earth onto mars it is possible to make predictions about the types of features that will be found on Mars, such as water and life. Thus, analogy is a very powerful mental tool to discover new things. As well as distinguishing between the Source and the Target researchers in analogical reasoning often distinguish between Superficial and Structural feature. Superficial features are things such as Mars being round or having a red hue. Thus, making an analogy between Mars and a red Stop sign would be an analogy based upon the feature red, which is a superficial attribute. Structural (or Relational features) refer to the underlying sets of relations between features (first order relations), or relations among relations (second and third order relations). In the case of Mars, structural relations might be the Seasonal movement of dark streaks across the surface of the planet and the presence of dust devils. Noting these attributes and relations led to the hypothesis that these are the same as dust devils on earth and that the same mechanisms that produce dust devil trails on earth are what is happening on Mars (As you can see analogy can be complicated). The major virtue of analogy is that it allows a person to go beyond the superficial. (Kevin Dunbar)

For a history of the use of term analogy by logicians and theologicians consult the Stanford Encyclopedia of Philosophy.