Boost::multi_index allows storing and accessing data in multiple ways simultaneously by maintaining multiple indices. It can index the same data by different fields, like id and name, without needing to duplicate or synchronize data. Users define the indices upfront, such as ordered by id and name. This allows efficient lookup and iteration by either field without additional containers or synchronization. Boost::multi_index provides common index types like ordered and hashed indices as well as tools to extract keys from objects. It offers powerful and flexible indexing of data.