As you browse the web, Internet Explorer "caches" (stores on your hard drive) the most recent sites you visited; this allows Internet Explorer to load your favorite sites faster, since it doesn't have to re-download images from the page every time you visit it. This is called your "browsing history", "cache", or "temporary internet files". Internet Explorer will automatically purge old files to accommodate caching new website you visit to stay under a certain size limit for all the files it caches. But you can, at any point, clear all this data, including the cached files, the URL's (internet addresses you visited, which are stored in the address bar), etc.
A separate tutorial is dedicated to showing you how to clear your cookies in Internet Explorer.
To clear your history in Internet Explorer, go to Safety > Delete Browsing History: this will open the brand new Delete Browsing History dialog, introduced in Internet Explorer 8. Unlike with previous versions of Internet Explorer, this new feature allows you to selectively delete your history. This means that you can target the pieces of history you want cleared, and not go through the inconvenience of deleting all your history. Internet Explorer 8 also introduces "InPrivate", a feature that allows you to navigate the web without leaving history traces after closing your browser window. We'll explain InPrivate later in this tutorial.
You can quickly open the Delete Browsing History dialog by pressing Ctrl+Shift+Del (which happens to be the same keyboard shortcut as Firefox).
Here are your options in deleting your browsing history and internet addresses:

This is otherwise known as Internet Explorer's "Auto Complete" feature; a properly designed form on the web (like a contact form), will leverage this feature in browsers that support it to minimize the amount of typing you need to complete the form in question. If you check this checkbox, all your autocomplete history will be deleted. (Another tutorial how to delete individual autocomplete pieces of data.)Once you have chosen which checkboxes to select, click on the Delete button: Internet Explorer will delete your browsing history based on the settings you chose - this should only take a few seconds, and the longest operation of them all is actually clearing the cache ("Temporary Internet Files"), since Internet Explorer has to delete the hundreds or thousands of files it has stored to let you surf the web faster.
The Delete Browsing History dialog will automatically close once Internet Explorer has finished clearing your cache, deleting cookies, removing recently visited addresses, etc.
Internet Explorer includes the option to automatically clear your cache once you close a browser window. Go to Tools > Internet Options, and look at the middle of the General tab options. Under Browsing history, Internet Explorer displays a "Delete browsing history on exit" checkbox, which is unchecked by default. To make Internet Explorer automatically delete your history when it exits, check the checkbox and click OK.