A philosophical principle that the likelihood function contains all the relevant information of the data for hypothesis testing.
If comparing a null and alternative, we might say that the comparison between two hypotheses should be based on their likelihoods. Put like this, the likelihood is principle is similar to, but weaker than, the law of likelihood. That is, one can adopt the likelihood principle but not the law of likelihood, but if one adopts the law of likelihood then you are implicitly adopting the likelihood principle as well.
Fisher, who didn’t require the notion of an alternative hypothesis (see Fisher’s paradigm), stated the likelihood principle as:
Likelihood serves all the purposes necessary for the problem of statistical estimation.