In e-commerce, a user tends to search for the desired product by issuing a query to the search engine and examining the retrieved results. If the search engine was successful in correctly understanding the user's query, it will return results that correspond to the products whose attributes match the terms in the query that are representative of the query's product intent. However, the search engine may fail to retrieve results that satisfy the query's product intent and thus degrading user experience due to different issues in query processing: (i) when multiple terms are present in a query it may fail to determine the relevant terms that are representative of the query's product intent, and (ii) it may suffer from vocabulary gap between the terms in the query and the product's description, i.e., terms used in the query are semantically similar but different from the terms in the product description. Hence, identifying the terms that describe the query's product intent and predicting additional terms that describe the query's product intent better than the existing query terms to the search engine is an essential task in e-commerce search. In this paper, we leverage the historical query reformulation logs of a major e-commerce retailer to develop distant-supervised approaches to solve both these problems. Our approaches exploit the fact that the significance of a term is dependent upon the context (other terms in the neighborhood) in which it is used in order to learn the importance of the term towards the query's product intent. We show that identifying and emphasizing the terms that define the query's product intent leads to a 3% improvement in ranking. Moreover, for the tasks of identifying the important terms in a query and for predicting the additional terms that represent product intent, experiments illustrate that our approaches outperform the non-contextual baselines.