ABC Music Notation, alias ABC code, is 'the text-based music notation system and the de facto standard for folk and traditional music.' (Chris Walshaw)
It is a simple text method of representing music. A benefit is that it can easily be stored on computers using ASCII characters, and conveyed by electronic means. Ideally it requires a simple program to interpret it into usable music notation or some form of audible sound.
There are literally tens of thousands of folk dance tunes (as well as other tune forms) in this format on the internet.
The best place to seek information on the ABC format and a list of software that uses it is at the ABC Homepage run by the developer, Chris Walshaw.
Another overview is in this Wikipedia article.
A quick way of getting a tune out of an abc file is to cut and paste the code into the interpreter at mandolintab.net
Some of the software required to access and use abc files requires a reasonable competence with computers but there are simple off -the-shelf solutions for those who just want to get going with the music.
Software packages (usually freeware) exist for most popular computer operating systems and also tools for mobile phones and tablets. The range can be found at http://abcnotation.com/software
This page will be expanded as necessary but there's enough here to get you started.