Transport security provides only point-to-point channel security. It means that HTTPS establish secure channel only between client and server exposed to client. But if this server is just a load balancer or proxy server it has direct access to content of the message.
Message security provides end-to-end channel security. It means that security is part of transferred data and only intended destination can decrypt the data (load balancer or proxy sees only encrypted message). Message security in most cases also uses certificates to provide encryption and signing but it is usually slower because transport security can use HW acceleration.