Refers to user-facing software written for monochrome terminal systems, such as IBM 3270 and 5250 terminals.
Typically these are legacy systems written for the mainframe or an AS/400. These apps were often written in RPG or COBOL or with special-purpose tools such as ISPF or even in SNOBOL. It is not uncommon for such apps to have single-page forms with dozens or even hundreds of input fields, which was the style at the time.
The term is used to distinguish between such systems and 'modern' browser-based front ends using HTML and PHP, Active Server Pages, or JavaServer Pages.
A special sort of application known as a screen scraper can be used to cruft an HTML front-end onto the green screen. The 'scraper' translates the user's input (often including an ASCII to EDB-CDIC transformation) and 'types' it into the green screen interface as if it were the user. Scrapers can also read the data off a green screen to pass it to newer Java or Windows applications.
As greenscreen (q.v.) the term refers to the entertainment industry's process devised for video chroma key matting.