Transport security is indeed very similar to HTTPS (and identical in many cases). What it provides you is an encrypted tunnel between your client and the server. Providing there's a direct connection from your client to your server, it's perfectly fine (providing that your client verifies that it got the right server certificate). If your client is talking to another intermediate server, on which you rely to pass the message to your server - then that intermediate server would get unencrypted data.
An example :
You have a company that processes payments. Because of some regulations, you need servers in each country, and those in turn pass the requests to your main server in the US.
You want to make sure that even if the local hosting company tries to find out what details are being passed, they can't.
That is what Message Security provides you - you trust only the client and your main servers, so you want only them to be able to encrypt and decrypt.
With Transport Security, there would be two transitions - the client will encrypt, and the intermediate server will decrypt. Then it will encrypt again, and your main servers will decrypt. As you can see, there is an intermediate phase where the data is plain in RAM in the intermediate server.
This MSDN article describes it very well, and where to use each :
MSDN