The days before the Internet required everyone to run software on their own hardware with their own operating system. Desktops and laptops still run this way most of the time. If a browser and Internet connection are now assumed then the flow of information from a web browser to a web server and back again can take the place of locally installed software. Tim O’Reilly is attributed with calling this Web 2.0 (wikipedia).
Mobile devices with their app stores are a different model, sometimes incorporating Internet hosted services within their custom-built for each platform applications. Each app’s code allows it to exploit the native capabilities of each device. Security is a concern as well. Is the app model a stop-gap measure on the way to providing all apps as web apps? Time will tell.