Files with .woff extension are files especially created for font creating. Its whole name means Web Open Font Format and it was created by W3C. Its main advantage is that it is not limited by some kind of license and W3C on its own is recommending using this file format as default file format of all font on web. This file type is mainly compressed OpenType or TrueType, but it is modified so there are some information delivered with it. The main plus is that it is supported by almost all browsers. We can use him in Internet Explorer by Microsoft, Google Chrome by Google, Mozilla Firefox created by Mozilla Foundation or even in Opera developed by Opera Software or in Apple´s Safari.
First version was released in 2009, but officially it was released on 27th June, 2010. Two years later on 13th December 2012 it was announced by W3C as ideal format for creation and use of fonts on web. Today it is in version 1.0, but version 2.0 was announced.
Opening and edit of these files saved in WOFF format can be achieved in Font Creator. For better work with this file format, it is much better to convert in on another type of files, modify it and then reformat it back. You can use almost every web browser to view these files.