A likelihood ratio test is useful for comparing the fit of a null model and an alternative model. The null model is a special case of the alternative model. The likelihood ratio expresses how many times more likely the data are under one model than the other. You can use the likelihood ratio or its logarithm to compute a p-value, or compare it to a critical value to decide whether to reject the null model in favor of the alternative model.
When you use the logarithm of the likelihood ratio, the statistic is known as the log-likelihood ratio statistic. You can use Wilks’s theorem to approximate the probability distribution of this statistic (assuming that the null model is true).