In Conceptual Metaphor, the target domain is the domain a listener is trying to understand or work with *by analogy to* concepts in the Source Domain.
Consider this diagram from Integer as a Metaphor:
(Double-click to enlarge)
The left side is the target domain. It is about computer arithmetic (nowadays, done on 64 bit words). The Source Domain is the mathematical idea of integers.
In this case, there's a problem because the source domain (mathematical integers) has no notion that there's a "biggest integer," whereas computer integers must. (This is way less important these days, but in the olden days, realistic calculations could easily overflow a machine word if you weren't careful.)