The Dis max query in Elasticsearch evaluates multiple queries and picks the highest score among them. It then adds a tie breaker value, which is a fraction of the other query scores, to the max score. This helps improve relevance when multiple queries match. In the example, two queries search for 'apple' in title and description fields. The first query scores 2.0, the second 1.5. The max score is 2.0. The tie breaker is 0.3, so 0.3 times 1.5 equals 0.45. Adding this to 2.0 gives a final score of 2.45. Variables like max_score, tie_breaker_sum, and final_score update step by step. This process ensures the best matching query dominates but others still influence the result slightly.