During a disaster event, two types of information that are especially useful for coordinating relief operations are needs and availabilities of resources (e.g., food, water, medicines) in the affected region. Information posted on microblogging sites is increasingly being used for assisting post-disaster relief operations. In this context, two practical challenges are (i)~to identify tweets that inform about resource needs and availabilities (termed as need-tweets and availability-tweets respectively), and (ii)~to automatically match needs with appropriate availabilities. While several works have addressed the first problem, there has been little work on automatically matching needs with availabilities. The few prior works that attempted matching only considered the resources, and no attempt has been made to understand other aspects of needs/availabilities that are essential for matching in practice. In this work, we develop a methodology for understanding five important aspects of need-tweets and availability-tweets, including what resource and what quantity is needed/available, the geographical location of the need/availability, and who needs / is providing the resource. Understanding these aspects helps us to address the need-availability matching problem considering not only the resources, but also other factors such as the geographical proximity between the need and the availability. To our knowledge, this study is the first attempt to develop methods for understanding the semantics of need-tweets and availability-tweets. We also develop a novel methodology for matching need-tweets with availability-tweets, considering both resource similarity and geographical proximity. Experiments on two datasets corresponding to two disaster events, demonstrate that our proposed methods perform substantially better matching than those in prior works.