First of all, the application layer is not where the actual applications on your computer function. These software applications sit on top of the OSI model and are not actually part of it. The application layer is the layer where protocols such as HTTP/HTTPS, FTP, SMTP, IMAP and others function. These protocols are then leveraged by software applications. This is what makes software applications “network aware” if you will.
From a practical standpoint, the model that is primarily used in today’s networks is the TCP/IP model. This model incorporates parts of the session and presentation layers into the transport and application layers resulting in a model with fewer layers.
So in your example of a web page, the web browser would use the HTTP protocol (Application layer) to communicate between the client (web browser) and the server (Web server). HTTP contains within its mechanisms the functionality of the presentation layer, so we don’t actually see the presentation layer in the Wireshark packet capture. The presentation functionalities essentially allow the information that is received from lower layers to be presented in a manner that the HTTP protocol, and the client can understand and display.
Similarly, the session layer functionalities are incorporated into the transport layer. The sessions that are being referred to here are those between the host and server, that is between the web browser and the web server and do not involve the sessions of any other hosts.
For more information about the TCP/IP model as compared to the OSI model, take a look at this lesson:
I hope this has been helpful!