MYSQL: What is the benefit of compound indexes, over separate ones?
If you know that you frequently query on a combination of fields, a combined index means "you only have to search one B-tree."  Otherwise, the server would have to search n individual B-trees and then combine the results.

(N.B.:  A "B-tree" is a data structure commonly used by database servers to create indexes ...)

(You can use the EXPLAIN command to quickly see how the server plans to do this ... and to see that it does have to do this.)