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In current web search engines, the relevance between a query and web pages (i.e. documents) is measured by Text Matching (TM) models. The documents retrieved mainly focus on matching text queries themselves but fail to find target information towards the user intent (e.g. the direct answer to question-style queries). Thus the document containing target information that users want may not be ranked at the top 1 in the search result or even not be recalled. Besides, as voice search and voice-powered assistants are entering our life, queries tend to be long tail ones, which needs a search engine evolved into a higher level of semantic relevance matching. Therefore, it is necessary to build an intent-target relevance matching model in modern search scenarios. This paper proposes a unified model of Machine Comprehension-incorporated Relevance Matching (MCRM). Totally, MCRM models how web users choose the relevant documents to read by observing the titles or summaries, and further look for target information from them. To accomplish that, we first formulate two tasks as Text Matching and Target Extracting. For learning each task, a Context-augmented Matching network (ContMatch) and a Matching-fused machine Comprehension network (MatComprehend) are proposed. Then, they are integrated into an end-to-end framework that can not only measure the semantic relevance but also extract the intent-related target, by deeply comprehending the semantics hidden in queries and exploiting intent-target relations between queries and documents. In MCRM, the two tasks are jointly learned by a multi-task learning approach, where the semantic relevance measured by ContMatch, and the intent-target relevance captured by MatComprehend, are combined and enhanced mutually for boosting the final performance. We conduct extensive experiments on real-world data. The experimental results demonstrate the superiority of MCRM against the state-of-the-art relevance models.