Well, WOFF is a new font standard, as you know (like truetype & opentype) but which is designed specifically for use on the web, to be embedded in HTML.
The reason this is significant; the reason you should care and the reason this development is on par with the invention of wearing underwear on the outside to save on laundry bills - is because the ability to embed fonts enables the using of fonts that may not be on the client's system. And WOFF fonts are optimised for this task.
So, while web sites have been limited to a small number of web safe fonts (eg Tahoma,Arial), with the new CSS rule font-face, the browser can now download a font and use it.
This may just sound like something for shandy-sipping, turtleneck-wearing designer-types - however, in some cases it's essential... like when an OS doesn't have a Japanese font, for example, and the web site has text in Japanese. This situation is ordinarily a dead-end, no-show.
WOFF format is the bees-knees for downloadable fonts, for 2 main reasons:
WOFF is compressed - smaller download sizes compared with raw TrueType or OpenType fonts. No need to manually gzip files or have the server do it
WOFF contains information that allows you to see where the font came from – without DRM – which has support from font creators
So,
Do we need it? Yes. We need another font system to cater for the need to compress and identify a font & work with embedding in web pages.
When? You would use WOFF in all cases when embedding web fonts (assuming browser support is ubiquitous)
Why? We wouldn't just stick to the existing ones because they are not compressed and can't be identified properly and cannot progress with the embeddable concept and are therefore not as suitable for the job.