I've never felt comfortable with the logical positivists' "science is prediction" characterization, primarily because it neglects what I intuitively think of as the heart of science: explanation. For example, Darwin's theory of evolution – perhaps the greatest scientific discovery ever – is big on explanation, but not nearly as big on prediction. (Because evolution happens on such long timescales, although microbial evolution can be observed on very short timescales.) Or consider the 'selfish gene' paradigm, the evolutionary paradigm of viewing the gene as fundamental unit of selection, and the organism as a mere tool fabricated by the genes for the purpose of propagating themselves into the future. Dawkins' discusses (I think it was in The Extended Phenotype) criticisms of the idea as not providing any new predictions. My initial reaction to these criticisms is always: So what? They're wonderful explanations of the world. They make sense of the world. Isn't that pretty remarkable?
The point I want to make here is that the emphasis on prediction is just a convenient special case of a more general principle: that a theory should correspond to reality, just as a map corresponds to the territory. Reality can be observed past, present, and future. It is just as well to vet a theory against past observations as against future observations. The reason the scientific method favors prediction is that it prevents the scientist from concocting a 'just so' story that too neatly fits the existing facts ("overfitting"). An idealized honest scientist can test a theory against any empirical evidence.
Darwin's theory is so amazing because it makes sense of so many existing facts. (And you can still make predictions about historical facts ("retrodictions"), such as the famous quip that evolution would be falsified by finding fossil rabbits in the precambrian.) Of course, if you have a beautiful theory that has no connection to reality, then you're not doing science. Science is concerned with explaining reality, and so scientific theories must say things about reality – things which can (in principle) be empirically checked. It ultimately doesn't matter where that evidence is temporally located.