Support curve is a statistical term, coined by A. W. F. Edwards, to describe the graph of the natural logarithm of the likelihood function. It has a relation to, but is distinct from the support of a distribution.
The function being plotted is used in the computation of the score and Fisher information, and the graph has a direct interpretation in the context of maximum likelihood estimation and likelihood-ratio tests.
The term refers to the hypotheses being tested, i.e. whether or not the data support one hypothesis (or parameter value) more than any other.
References
Support curve Wikipedia(Text) CC BY-SA