CockroachDB uses indexes to efficiently organize and retrieve data from SQL tables, allowing for faster queries by reducing the need to scan entire tables. Indexes are additional structures that organize data according to specific columns, making searches based on those columns more efficient. For example, an index on the "Artist" column in a songs database allows for quick retrieval of songs by a particular artist. Different types of indexes, such as covering and non-covering indexes, affect query efficiency based on whether all necessary columns are included in the index. The choice of index depends on various factors, including the desired search space restriction, result ordering, and whether an index covers all the queried columns. Index selection is critical for optimizing query performance, and CockroachDB provides ways to guide index usage through hints. Future improvements to CockroachDB aim to incorporate dynamic factors like table sizes and query feedback to enhance index selection further.