Given a piece of evidence and two hypotheses and the likelihood ratio between them is the ratio of the likelihood each hypothesis assigns to
For example, imagine the evidence is = "Mr. Boddy was knifed", and the hypotheses are = "Professor Plum did it" and = "Mrs. White did it." Let's say that, if Professor Plum were the killer, we're 25% sure he would have used a knife. Let's also say that, if Mrs. White were the killer, there's only a 5% chance she would have used a knife. Then the likelihood ratio of between and is 25/5 = 5, which says that assigns five times as much likelihood to as does which means that the evidence supports the "Plum did it" hypothesis five times as much as it supports the "Mrs. White did it" hypothesis.
A likelihood ratio of 5 denotes relative likelihoods of Relative likelihoods can be multiplied by odds in order to update those odds, as per Bayes' rule.