A portal page is made of a set of portlets. For example, the portal page such as Welcome contains portlets such as Navigation, Language, and so on And the portlet Language has icons (such as Look and Feel, Configuration, Minimize, Maximize, and Remove), title icon and title (such as Language), and a window which may contain contents (such as a set of language icons and links).
In a normal way, a portlet is an application that provides some content (such as information or service) that forms part of a portal page. A portlet container handles the portlets. A portlet container also processes requests and generates dynamic content. Actually, portals use portlets as pluggable user interface to provide a presentation layer information.
Loosely speaking, portlets are fragments of an HTML page, that is pieces of markup (such as HTML, XHTML, WML, and so on). The content of a portlet is normally aggregated with the content of other portlets to form the portal page. The lifecycle of a portlet is managed by the portlet container. The content generated by a portlet may vary from one user to another, depending on the user configuration for the portlet.
I might even add a new term to your query: "Portlet application"
An application itself can be anything. In the Windows world, it's an executable. On the web, it's probably a bunch of Servlets and JSPs working together.
On the portal, we use the term portal application. A portal or portlet application would be multiple individual portlets that are packaged in a common war file, that together provide a common user experience. So, a tax preparation portlet application might have a few portlets: one that helps you do your taxes, another that shows you retirement investment plans, another that provides tax savings tips, and another that provides various payment schedules for loans or mortgages. It is very conceivable that a tax planning application might have these various features. On the portal, each would be provided as perhaps an individual portlet, or window, that provides specific details, but can work with other portlets that are part of a portal application.
Having said that, a portal page might have portlets from varios different portlet applications. Just look at facebook or a yahoo portal. Those pages have many portlets providing information, although each individual portlet might be packaged and deployed in a separate war, aka portal application.