The Wiki has a good definition along with some examples:
As a concrete example of a classic screen scraper, consider a hypothetical legacy system dating from the 1960s -- the dawn of computerized data processing. Computer to user interfaces from that era were often simply text-based dumb terminals which were not much more than virtual teleprinters. (Such systems are still in use today, for various reasons.) The desire to interface such a system to more modern systems is common. An elegant solution will often require things no longer available, such as source code, system documentation, APIs, and/or programmers with experience in a 45 year old computer system. In such cases, the only feasible solution may be to write a screen scraper which "pretends" to be a user at a terminal. The screen scraper might connect to the legacy system via Telnet, emulate the keystrokes needed to navigate the old user interface, process the resulting display output, extract the desired data, and pass it on to the modern system.
Modern web scrapers are much easier to find. For example, there are numerous programs and utilities which query commercial web sites (e.g., Google Product Search) to get product information and display it out of the context of the commercial service. Such usage is also an example of why some web-site operators see web scraping as undesirable. A popular method to protect a site from being web scraped is the use of CAPTCHA, which attempts to block automated access to a website.