Application and Transport are two of the seven layers in the OSI reference model for computer networks.
Notably, the Internet does not use the full seven layer OSI model and it can be argued that it is really a 5 layer model rather than a 7 layer one (Session and Presentation are not really used as the Application can use protocols in the the transport layer (TCP/IP) directly).
The idea behind having different layers is that they can often be interchanged, and generally don't care about what happens below. That way, if you're using a dialup modem connection, or WiFi, your application will continue to operate the same way (although at the low levels, you might be using an entirely different method of communication).
In modern operating systems, the application generally talks to the operating system's 'network stack' to get a session (e.g. a TCP connection). The program running in user space is the 'Application Layer'.
Sometimes people build things on top of other protocols. So in the case of HTTP (used by web browser) it can also be used as a transport protocol. It is an application level protocol in its own right, but can be used as a transport protocol instead of TCP/IP.