Videos in the GIF format will save you data and possibly compresses the size of the file ( I am not sure, maybe those who know the details can put in their views in that regard here) and that could be one of the reasons for the widespread use of GIFs. Moreover, WhatsApp videos and images are generally "Forwarded as Received" kind of thing. So I would guess, that can explain the surge in the usage of GIFs.
Live....and Let Live!
GIF is Graphic Interchange Format. It is like a small videographic presentation that places small individual images and represent them serially almost like a video.
Coming to creating a GIF of your own, you can create them in Photoshop or through any other graphic designing software and save a set of related images as GIF.