These are not really "videos" but animated GIFs. It is an image file like JPG and TIFF, except they move. They work like "flip books" which consists of a series of similar pictures with slightly different changes eg. arms swinging and legs moving.
Many fellow TERBies have such animated GIFs in their signatures.
You can save these animated GIFs (eg. on giftube) by right-clicking over it -> "save image as". It will save as a GIF file. Then you can attach it to an email just like attaching a Word document etc.
